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Solve equation containing sine and exponential function for x
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leaving the context behind, I simplified a problem to the following equation:
solve for x: $$e^frac-xa cdot sin(b + cx) = sin(b)$$
Since my equations contains both sine and exponential function, I could neither use $ln$ nor $sin(x)^-1$. I tried using eulers identity to reduce all sine functions to exponential functions. Sadly, this couldn't help me either.
Thanks in advance.
analysis
asked Jul 21 at 21:46
CS_1994
92
add a comment |Â
up vote
1
down vote
favorite
leaving the context behind, I simplified a problem to the following equation:
solve for x: $$e^frac-xa cdot sin(b + cx) = sin(b)$$
Since my equations contains both sine and exponential function, I could neither use $ln$ nor $sin(x)^-1$. I tried using eulers identity to reduce all sine functions to exponential functions. Sadly, this couldn't help me either.
Thanks in advance.
analysis
asked Jul 21 at 21:46
CS_1994
92
Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
leaving the context behind, I simplified a problem to the following equation:
solve for x: $$e^frac-xa cdot sin(b + cx) = sin(b)$$
Since my equations contains both sine and exponential function, I could neither use $ln$ nor $sin(x)^-1$. I tried using eulers identity to reduce all sine functions to exponential functions. Sadly, this couldn't help me either.
Thanks in advance.
analysis
asked Jul 21 at 21:46
CS_1994
92
leaving the context behind, I simplified a problem to the following equation:
solve for x: $$e^frac-xa cdot sin(b + cx) = sin(b)$$
Since my equations contains both sine and exponential function, I could neither use $ln$ nor $sin(x)^-1$. I tried using eulers identity to reduce all sine functions to exponential functions. Sadly, this couldn't help me either.
Thanks in advance.
analysis
asked Jul 21 at 21:46
CS_1994
92
edited Jul 21 at 22:49
asked Jul 21 at 21:46
CS_1994
92
asked Jul 21 at 21:46
CS_1994
92
asked Jul 21 at 21:46
CS_1994
92
92
Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08
add a comment |Â
Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08
Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
You can rewrite this into
$$
f(x) = e^-x/a sin(b + cx) - sin(a)
$$
and look for the roots.
$f$ seems to be a variation of a sine function modulated by an exponential function.
E.g.
Looks like a signal from electrical engineering.
Maybe they have a non-numerical solution?
answered Jul 21 at 22:26
mvw
30.3k22250
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
You can rewrite this into
$$
f(x) = e^-x/a sin(b + cx) - sin(a)
$$
and look for the roots.
$f$ seems to be a variation of a sine function modulated by an exponential function.
E.g.
Looks like a signal from electrical engineering.
Maybe they have a non-numerical solution?
answered Jul 21 at 22:26
mvw
30.3k22250
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
add a comment |Â
up vote
0
down vote
You can rewrite this into
$$
f(x) = e^-x/a sin(b + cx) - sin(a)
$$
and look for the roots.
$f$ seems to be a variation of a sine function modulated by an exponential function.
E.g.
Looks like a signal from electrical engineering.
Maybe they have a non-numerical solution?
answered Jul 21 at 22:26
mvw
30.3k22250
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
add a comment |Â
up vote
0
down vote
up vote
0
down vote
You can rewrite this into
$$
f(x) = e^-x/a sin(b + cx) - sin(a)
$$
and look for the roots.
$f$ seems to be a variation of a sine function modulated by an exponential function.
E.g.
Looks like a signal from electrical engineering.
Maybe they have a non-numerical solution?
answered Jul 21 at 22:26
mvw
30.3k22250
You can rewrite this into
$$
f(x) = e^-x/a sin(b + cx) - sin(a)
$$
and look for the roots.
$f$ seems to be a variation of a sine function modulated by an exponential function.
E.g.
Looks like a signal from electrical engineering.
Maybe they have a non-numerical solution?
answered Jul 21 at 22:26
mvw
30.3k22250
answered Jul 21 at 22:26
mvw
30.3k22250
answered Jul 21 at 22:26
mvw
30.3k22250
answered Jul 21 at 22:26
mvw
30.3k22250
30.3k22250
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
add a comment |Â
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
I'm sorry for my late edit, the last part is $sin(b)$. Indeed, it is. The problem is the following. I want to know if a certain value $y_0$ or $y(x=0)$ returns in $y(x) = r cdot e^frac-xa cdot sin(b + cx)$. Writing this as a equation, I get the one from above. I am able to get to a solution numerically, but it would be satisfying if there was a mathematical solution.
– CS_1994
Jul 21 at 23:14
add a comment |Â
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Can you pick $c$ arbitrarily? It then has a solution for certain choice of it.
– Tolga Birdal
Jul 21 at 22:14
Well, c is given. Specified, c is an angular frequency $omega = 2 pi f$. There is a specific case in which $w = 2 pi 83$, but it would be nice To have a General solution.
– CS_1994
Jul 21 at 22:40
How about $b$ and $a$? Are these quantities related to $c$? I guess this matters for a general solution.
– Tolga Birdal
Jul 21 at 22:54
$a$ and $b$ are not related to $c$. $a$ is a time-constant, $a in mathbb R_+$. $b in [0, 2pi)$ or $b in [0°, 360°)$
– CS_1994
Jul 21 at 23:08