Find the general solution to: $$x'' + 2c \; x' + \left( \frac{2}{\cosh^2 t} - 1\right)x =0$$ where $c$ is a constant.
A linear differential equation
2
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ordinary-differential-equations
recreational-mathematics
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0In order to get the best possible answers, it is helpful if you say what your thoughts on the problem are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level. Also, people are much happier to help those who demonstrate that they've tried the problem themselves first. – 2012-06-23
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1@ZevChonoles I know this poem, as well as a solution. I though some of math.SE users would find this problem interesting :| – 2012-06-23
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1The fact that you know a solution is *definitely* something that ought to be mentioned. Why not post it as an answer to your question, so that others don't waste their time explaining that solution to you? If someone knows a different method of solving the problem they can still post it. – 2012-06-23
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0There's nothing wrong with asking questions you know the answer to, as long as you indicate that fact. [See this meta discussion](http://meta.math.stackexchange.com/questions/4232/is-it-okay-to-ask-mathematical-puzzles-and-problems-i-have-solved#comment16214_4233). – 2012-06-23
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0@ZevChonoles so here goes the tag. I think submitting my own solution would spoil the problem a bit. – 2012-06-23
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0I understand your reasoning. Would posting it [behind a spoiler block](http://meta.stackoverflow.com/editing-help#spoilers) be amenable to you? – 2012-06-23
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0@ZevChonoles maybe I should just delete this topic? I didn't know that posting some (imho) interesting problems will be such a trouble. – 2012-06-23
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3There's no need to delete - and I apologize if was coming across a bit harsh. I just feel that the origin of a problem is an important part of what should go into a post - whether it's homework, research, for fun, or anything else, one should explain where the problem is coming from. As long as that information is included, I'd love to keep this question open so that people can try their hand at it. – 2012-06-23
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0Would you mind posting the solution since nobody answered? I would really like knowing the answer. Thank you, rubik – 2012-06-25
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0@rubik ok, here it goes. – 2012-06-25