How to rewrite exponential function $e^x+c$ into $ce^x$? [closed]

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Tried to rewrite $e^x+c$ by using exponential properties $e^x.e^c=e^x+c$ but struggle to understand how to get into $ce^x$. Is it always the case that $c=e^c$?

Edit: To put in context, I solved a separable differential equation $fracdydx=y$, I get the solution is $y = e^x+c$. But the solution in the book is written $y=ce^x$.

differential-equations

share|cite|improve this question

edited Jul 18 at 20:22

asked Jul 17 at 21:05

reckn

72

closed as off-topic by Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus Jul 18 at 1:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
  – Math Lover
  Jul 17 at 21:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $e^x+c = e^ce^x$. Now define $C:=e^c$.
  – amsmath
  Jul 17 at 21:08
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
  – Xander Henderson
  Jul 18 at 0:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
  – Xander Henderson
  Jul 18 at 0:49
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
  – reckn
  Jul 18 at 20:30
  
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

Tried to rewrite $e^x+c$ by using exponential properties $e^x.e^c=e^x+c$ but struggle to understand how to get into $ce^x$. Is it always the case that $c=e^c$?

Edit: To put in context, I solved a separable differential equation $fracdydx=y$, I get the solution is $y = e^x+c$. But the solution in the book is written $y=ce^x$.

differential-equations

share|cite|improve this question

edited Jul 18 at 20:22

asked Jul 17 at 21:05

reckn

72

closed as off-topic by Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus Jul 18 at 1:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
  – Math Lover
  Jul 17 at 21:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $e^x+c = e^ce^x$. Now define $C:=e^c$.
  – amsmath
  Jul 17 at 21:08
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
  – Xander Henderson
  Jul 18 at 0:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
  – Xander Henderson
  Jul 18 at 0:49
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
  – reckn
  Jul 18 at 20:30
  
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

Tried to rewrite $e^x+c$ by using exponential properties $e^x.e^c=e^x+c$ but struggle to understand how to get into $ce^x$. Is it always the case that $c=e^c$?

Edit: To put in context, I solved a separable differential equation $fracdydx=y$, I get the solution is $y = e^x+c$. But the solution in the book is written $y=ce^x$.

differential-equations

share|cite|improve this question

edited Jul 18 at 20:22

asked Jul 17 at 21:05

reckn

72

Tried to rewrite $e^x+c$ by using exponential properties $e^x.e^c=e^x+c$ but struggle to understand how to get into $ce^x$. Is it always the case that $c=e^c$?

Edit: To put in context, I solved a separable differential equation $fracdydx=y$, I get the solution is $y = e^x+c$. But the solution in the book is written $y=ce^x$.

differential-equations

share|cite|improve this question

edited Jul 18 at 20:22

asked Jul 17 at 21:05

reckn

72

share|cite|improve this question

share|cite|improve this question

edited Jul 18 at 20:22

edited Jul 18 at 20:22

edited Jul 18 at 20:22

asked Jul 17 at 21:05

reckn

72

asked Jul 17 at 21:05

reckn

72

asked Jul 17 at 21:05

reckn

72

72

closed as off-topic by Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus Jul 18 at 1:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus Jul 18 at 1:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, amWhy, Xander Henderson, Isaac Browne, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
  – Math Lover
  Jul 17 at 21:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $e^x+c = e^ce^x$. Now define $C:=e^c$.
  – amsmath
  Jul 17 at 21:08
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
  – Xander Henderson
  Jul 18 at 0:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
  – Xander Henderson
  Jul 18 at 0:49
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
  – reckn
  Jul 18 at 20:30
  
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
  – Math Lover
  Jul 17 at 21:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $e^x+c = e^ce^x$. Now define $C:=e^c$.
  – amsmath
  Jul 17 at 21:08
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
  – Xander Henderson
  Jul 18 at 0:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
  – Xander Henderson
  Jul 18 at 0:49
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
  – reckn
  Jul 18 at 20:30
  
  

  
  
  
  

1

1

Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
– Math Lover
Jul 17 at 21:07

Note that if $C=e^c$ then $e^x+c=e^ccdot e^x=C e^x$.
– Math Lover
Jul 17 at 21:07

1

1

$e^x+c = e^ce^x$. Now define $C:=e^c$.
– amsmath
Jul 17 at 21:08

$e^x+c = e^ce^x$. Now define $C:=e^c$.
– amsmath
Jul 17 at 21:08

1

1

It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
– Xander Henderson
Jul 18 at 0:48

It would be really helpful if you could provide some additional context. My guess is that this is popping up in an elementary calculus or differential equations class, where the solution to some DE is of the form $mathrme^x+c$, where $c$ is some constant of integration, which ultimately depends on some initial condition. As others have pointed out, $mathrme^c$ is then also a constant depending on the initial condition, so it does no harm to relabel the constants and set $c = mathrme^c$ (where the $c$ on the left is different from the $c$ on the right).
– Xander Henderson
Jul 18 at 0:48

If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
– Xander Henderson
Jul 18 at 0:49

If you are worried about keeping track of the constants, perhaps write $$mathrme^x + C_1 = mathrme^C_1 mathrme^x = C_2 mathrme^x, $$ where both $C_1$ and $C_2$ are constant, subject to the relation $C_2 := mathrme^C_1$.
– Xander Henderson
Jul 18 at 0:49

@XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
– reckn
Jul 18 at 20:30

@XanderHenderson Yes, I'm trying to solve a differential equation $fracdydx=y$. By the way, can you helped me to understand in which situation that we can't relabel $c=e^c$. Thanks for your comment, I've edited my question.
– reckn
Jul 18 at 20:30

 | 
show 1 more comment

2 Answers
2

active

oldest

votes

up vote
1
down vote

It truly is :

$$e^x+c = e^c cdot e^x$$

Now, if you simply manipulate the constant $c$ to be $c := e^c$ the expression becomes the desired :

$$boxede^x+c = ce^x$$

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

add a comment | 

up vote
0
down vote

Hint

If $c$ is a constant then $e^c$ is still a constant.

Note that in mathematics constant are arbitrary: if a call $c$ a constant and then take $c+1$ I can still call it $c$ (note that this doesn't mean that they are the same constant, but nontheless both of them are a constant)

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
  – reckn
  Jul 17 at 21:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
  – Davide Morgante
  Jul 17 at 21:36
  
  

  
  
  
  

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

It truly is :

$$e^x+c = e^c cdot e^x$$

Now, if you simply manipulate the constant $c$ to be $c := e^c$ the expression becomes the desired :

$$boxede^x+c = ce^x$$

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

add a comment | 

up vote
1
down vote

It truly is :

$$e^x+c = e^c cdot e^x$$

Now, if you simply manipulate the constant $c$ to be $c := e^c$ the expression becomes the desired :

$$boxede^x+c = ce^x$$

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

add a comment | 

up vote
1
down vote

up vote
1
down vote

It truly is :

$$e^x+c = e^c cdot e^x$$

Now, if you simply manipulate the constant $c$ to be $c := e^c$ the expression becomes the desired :

$$boxede^x+c = ce^x$$

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

It truly is :

$$e^x+c = e^c cdot e^x$$

Now, if you simply manipulate the constant $c$ to be $c := e^c$ the expression becomes the desired :

$$boxede^x+c = ce^x$$

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

share|cite|improve this answer

share|cite|improve this answer

answered Jul 17 at 21:07

Rebellos

10k21039

answered Jul 17 at 21:07

Rebellos

10k21039

answered Jul 17 at 21:07

Rebellos

10k21039

10k21039

add a comment | 

add a comment | 

up vote
0
down vote

Hint

If $c$ is a constant then $e^c$ is still a constant.

Note that in mathematics constant are arbitrary: if a call $c$ a constant and then take $c+1$ I can still call it $c$ (note that this doesn't mean that they are the same constant, but nontheless both of them are a constant)

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
  – reckn
  Jul 17 at 21:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
  – Davide Morgante
  Jul 17 at 21:36
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

Hint

If $c$ is a constant then $e^c$ is still a constant.

Note that in mathematics constant are arbitrary: if a call $c$ a constant and then take $c+1$ I can still call it $c$ (note that this doesn't mean that they are the same constant, but nontheless both of them are a constant)

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
  – reckn
  Jul 17 at 21:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
  – Davide Morgante
  Jul 17 at 21:36
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

Hint

If $c$ is a constant then $e^c$ is still a constant.

Note that in mathematics constant are arbitrary: if a call $c$ a constant and then take $c+1$ I can still call it $c$ (note that this doesn't mean that they are the same constant, but nontheless both of them are a constant)

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

Hint

If $c$ is a constant then $e^c$ is still a constant.

Note that in mathematics constant are arbitrary: if a call $c$ a constant and then take $c+1$ I can still call it $c$ (note that this doesn't mean that they are the same constant, but nontheless both of them are a constant)

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

share|cite|improve this answer

share|cite|improve this answer

answered Jul 17 at 21:09

Davide Morgante

1,875220

answered Jul 17 at 21:09

Davide Morgante

1,875220

answered Jul 17 at 21:09

Davide Morgante

1,875220

1,875220

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
  – reckn
  Jul 17 at 21:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
  – Davide Morgante
  Jul 17 at 21:36
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
  – reckn
  Jul 17 at 21:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
  – Davide Morgante
  Jul 17 at 21:36
  
  

  
  
  
  

Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
– reckn
Jul 17 at 21:35

Does it mean constant function such $e^c, (c + 11), 3c, sqrtc$, etc is also a constant?
– reckn
Jul 17 at 21:35

@Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
– Davide Morgante
Jul 17 at 21:36

@Inrtia Yes they are! At the end of the day if $c$ is a number, you can do anything you want whit it and it will remain a number no matter what
– Davide Morgante
Jul 17 at 21:36

add a comment |