Mixing
Solving inhomogeneous ode with non-constant coefficients [closed]
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Do we have an explicit solution up to some constant for inhomogenous ODE with non-constant coefficients?
ordinary-differential-equations
asked Jan 20 at 17:13
AngelaAngela
61
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closed as off-topic by Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh Jan 21 at 0:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
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If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Do we have an explicit solution up to some constant for inhomogenous ODE with non-constant coefficients?
ordinary-differential-equations
asked Jan 20 at 17:13
AngelaAngela
61
$endgroup$
closed as off-topic by Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh Jan 21 at 0:10
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
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Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
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– Dog_69
Jan 20 at 17:41
add a comment |
$begingroup$
Do we have an explicit solution up to some constant for inhomogenous ODE with non-constant coefficients?
ordinary-differential-equations
asked Jan 20 at 17:13
AngelaAngela
61
$endgroup$
Do we have an explicit solution up to some constant for inhomogenous ODE with non-constant coefficients?
ordinary-differential-equations
ordinary-differential-equations
asked Jan 20 at 17:13
AngelaAngela
61
asked Jan 20 at 17:13
AngelaAngela
61
asked Jan 20 at 17:13
AngelaAngela
61
asked Jan 20 at 17:13
AngelaAngela
61
asked Jan 20 at 17:13
AngelaAngela
61
61
closed as off-topic by Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh Jan 21 at 0:10
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh Jan 21 at 0:10
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, max_zorn, verret, José Carlos Santos, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
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Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
$endgroup$
– Dog_69
Jan 20 at 17:41
add a comment |
2
$begingroup$
Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
$endgroup$
– Dog_69
Jan 20 at 17:41
2
2
$begingroup$
Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
$endgroup$
– Dog_69
Jan 20 at 17:41
$begingroup$
Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
$endgroup$
– Dog_69
Jan 20 at 17:41
add a comment |
1 Answer
1
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oldest
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Sometimes yes, sometimes no. It depends on the equation.
EDIT: For example, $y'' + y/x^2 = x^2$ has general solution
$$ y = a sqrt{x} cosleft(frac{sqrt{3}}{2} ln(x)right) +
b sqrt{x} sinleft(frac{sqrt{3}}{2} ln(x)right) + frac{x^4}{13}$$
for arbitrary constants $a, b$.
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
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Thank you, could you pls give me one example for having solution
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– Angela
Jan 20 at 17:26
1
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The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
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– John Barber
Jan 20 at 17:50
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Sorry, yes, that was a typo.
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– Robert Israel
Jan 20 at 19:35
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Sometimes yes, sometimes no. It depends on the equation.
EDIT: For example, $y'' + y/x^2 = x^2$ has general solution
$$ y = a sqrt{x} cosleft(frac{sqrt{3}}{2} ln(x)right) +
b sqrt{x} sinleft(frac{sqrt{3}}{2} ln(x)right) + frac{x^4}{13}$$
for arbitrary constants $a, b$.
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
$endgroup$
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
1
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
add a comment |
$begingroup$
Sometimes yes, sometimes no. It depends on the equation.
EDIT: For example, $y'' + y/x^2 = x^2$ has general solution
$$ y = a sqrt{x} cosleft(frac{sqrt{3}}{2} ln(x)right) +
b sqrt{x} sinleft(frac{sqrt{3}}{2} ln(x)right) + frac{x^4}{13}$$
for arbitrary constants $a, b$.
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
$endgroup$
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
1
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
add a comment |
$begingroup$
Sometimes yes, sometimes no. It depends on the equation.
EDIT: For example, $y'' + y/x^2 = x^2$ has general solution
$$ y = a sqrt{x} cosleft(frac{sqrt{3}}{2} ln(x)right) +
b sqrt{x} sinleft(frac{sqrt{3}}{2} ln(x)right) + frac{x^4}{13}$$
for arbitrary constants $a, b$.
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
$endgroup$
Sometimes yes, sometimes no. It depends on the equation.
EDIT: For example, $y'' + y/x^2 = x^2$ has general solution
$$ y = a sqrt{x} cosleft(frac{sqrt{3}}{2} ln(x)right) +
b sqrt{x} sinleft(frac{sqrt{3}}{2} ln(x)right) + frac{x^4}{13}$$
for arbitrary constants $a, b$.
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
edited Jan 20 at 19:35
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
answered Jan 20 at 17:23
Robert IsraelRobert Israel
326k23215469
326k23215469
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
1
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
add a comment |
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
1
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
$begingroup$
Thank you, could you pls give me one example for having solution
$endgroup$
– Angela
Jan 20 at 17:26
1
1
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
The example solution doesn't solve the example ODE when $a = b = 0$. I think you may have solved it with an $x^2$ on the right hand side.
$endgroup$
– John Barber
Jan 20 at 17:50
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
$begingroup$
Sorry, yes, that was a typo.
$endgroup$
– Robert Israel
Jan 20 at 19:35
add a comment |
2
$begingroup$
Welcome to M.SE! In order to get a satisfaccotry answer, I suggest you to include more details to your answer. For example, what is the motivation of your question?
$endgroup$
– Dog_69
Jan 20 at 17:41