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Non-Linear ordinary differential equation involving first derivative [closed]
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Kindly help me in solving non-linear ODE:
$$y'^2+y^2+4=0$$
differential-equations
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
asked Jul 22 at 8:33
Adeel
62
closed as off-topic by Parcly Taxel, José Carlos Santos, Shailesh, Siong Thye Goh, quid♦ Jul 22 at 10:02
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." РParcly Taxel, Jos̩ Carlos Santos, Shailesh, Siong Thye Goh, quid
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up vote
1
down vote
favorite
Kindly help me in solving non-linear ODE:
$$y'^2+y^2+4=0$$
differential-equations
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
asked Jul 22 at 8:33
Adeel
62
closed as off-topic by Parcly Taxel, José Carlos Santos, Shailesh, Siong Thye Goh, quid♦ Jul 22 at 10:02
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." РParcly Taxel, Jos̩ Carlos Santos, Shailesh, Siong Thye Goh, quid
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
4
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Kindly help me in solving non-linear ODE:
$$y'^2+y^2+4=0$$
differential-equations
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
asked Jul 22 at 8:33
Adeel
62
Kindly help me in solving non-linear ODE:
$$y'^2+y^2+4=0$$
differential-equations
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
asked Jul 22 at 8:33
Adeel
62
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
edited Jul 22 at 8:35
Parcly Taxel
33.6k136588
33.6k136588
asked Jul 22 at 8:33
Adeel
62
asked Jul 22 at 8:33
Adeel
62
asked Jul 22 at 8:33
Adeel
62
62
closed as off-topic by Parcly Taxel, José Carlos Santos, Shailesh, Siong Thye Goh, quid♦ Jul 22 at 10:02
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." РParcly Taxel, Jos̩ Carlos Santos, Shailesh, Siong Thye Goh, quid
closed as off-topic by Parcly Taxel, José Carlos Santos, Shailesh, Siong Thye Goh, quid♦ Jul 22 at 10:02
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." РParcly Taxel, Jos̩ Carlos Santos, Shailesh, Siong Thye Goh, quid
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
4
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37
add a comment |Â
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
4
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
4
4
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37
add a comment |Â
1 Answer
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Substitute $y=2sinh u$ therefore $$4u'^2cosh^2u+4+4sinh^2u=0$$which means that $$4u'^2cosh^2u+4cosh^2u=0$$since $cosh(.)$ is always positive we obtain $$u'^2+1=0$$which has no real answer, but if whole the complex plane is included then$$u'=begincasesi& ,xin S\-i& ,xnotin Sendcases$$where $i=sqrt -1$ and at least one of $S$ or $S^c$ is homeomorphic to $Bbb N$ (you don't need to mind this constraint so much, just choose $S$ so that $u$ is integrable). One answer is $$u=begincasesix& ,xin S\-ix& ,xnotin Sendcases$$which leads to $$y=begincasesisin x& ,xin S\-isin x& ,xnotin Sendcases$$
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Substitute $y=2sinh u$ therefore $$4u'^2cosh^2u+4+4sinh^2u=0$$which means that $$4u'^2cosh^2u+4cosh^2u=0$$since $cosh(.)$ is always positive we obtain $$u'^2+1=0$$which has no real answer, but if whole the complex plane is included then$$u'=begincasesi& ,xin S\-i& ,xnotin Sendcases$$where $i=sqrt -1$ and at least one of $S$ or $S^c$ is homeomorphic to $Bbb N$ (you don't need to mind this constraint so much, just choose $S$ so that $u$ is integrable). One answer is $$u=begincasesix& ,xin S\-ix& ,xnotin Sendcases$$which leads to $$y=begincasesisin x& ,xin S\-isin x& ,xnotin Sendcases$$
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
add a comment |Â
up vote
1
down vote
Substitute $y=2sinh u$ therefore $$4u'^2cosh^2u+4+4sinh^2u=0$$which means that $$4u'^2cosh^2u+4cosh^2u=0$$since $cosh(.)$ is always positive we obtain $$u'^2+1=0$$which has no real answer, but if whole the complex plane is included then$$u'=begincasesi& ,xin S\-i& ,xnotin Sendcases$$where $i=sqrt -1$ and at least one of $S$ or $S^c$ is homeomorphic to $Bbb N$ (you don't need to mind this constraint so much, just choose $S$ so that $u$ is integrable). One answer is $$u=begincasesix& ,xin S\-ix& ,xnotin Sendcases$$which leads to $$y=begincasesisin x& ,xin S\-isin x& ,xnotin Sendcases$$
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Substitute $y=2sinh u$ therefore $$4u'^2cosh^2u+4+4sinh^2u=0$$which means that $$4u'^2cosh^2u+4cosh^2u=0$$since $cosh(.)$ is always positive we obtain $$u'^2+1=0$$which has no real answer, but if whole the complex plane is included then$$u'=begincasesi& ,xin S\-i& ,xnotin Sendcases$$where $i=sqrt -1$ and at least one of $S$ or $S^c$ is homeomorphic to $Bbb N$ (you don't need to mind this constraint so much, just choose $S$ so that $u$ is integrable). One answer is $$u=begincasesix& ,xin S\-ix& ,xnotin Sendcases$$which leads to $$y=begincasesisin x& ,xin S\-isin x& ,xnotin Sendcases$$
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
Substitute $y=2sinh u$ therefore $$4u'^2cosh^2u+4+4sinh^2u=0$$which means that $$4u'^2cosh^2u+4cosh^2u=0$$since $cosh(.)$ is always positive we obtain $$u'^2+1=0$$which has no real answer, but if whole the complex plane is included then$$u'=begincasesi& ,xin S\-i& ,xnotin Sendcases$$where $i=sqrt -1$ and at least one of $S$ or $S^c$ is homeomorphic to $Bbb N$ (you don't need to mind this constraint so much, just choose $S$ so that $u$ is integrable). One answer is $$u=begincasesix& ,xin S\-ix& ,xnotin Sendcases$$which leads to $$y=begincasesisin x& ,xin S\-isin x& ,xnotin Sendcases$$
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
edited Jul 22 at 8:50
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
answered Jul 22 at 8:43
Mostafa Ayaz
8,5773630
8,5773630
add a comment |Â
add a comment |Â
Welcome tu MSE. Before posting questions you should take a look at our community guidelines on how to write better questions. Let us know that you've tried to solve the problem and post your solution even if it's not correct or you're stuck somewhere
– Davide Morgante
Jul 22 at 8:36
4
How peculiar, the LHS is always positive; so no real solutions.
– Lord Shark the Unknown
Jul 22 at 8:37