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I was wondering if I had a solution $w$ to $w^{(4)} +w'' + w^3 = 0$, is it possible to get a solution to $u^{(4)} + u^3 = 0$ using $w$. Basically I am wondering if it is possible to manipulate $w$ in some manner to get a solution to the second ode (perhaps by adding and multiplying $w$ by some function or taking some sort of composition). I hope my question is clear. Thanks in advanced.

John
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  • Is this an attempt to tackle your older question? I don't see a way to relate these two equations; what made you think of $w^{(4)}+w''+w^3=0$ specifically? – 75064 May 08 '13 at 15:20
  • I'm actually more interested in this equation. I was trying to use solutions to $u^{(4)}+u^3=0$ to help show blowup of $w^{(4)}+w''+w^3=0$. I don't see a way to relate them either. – John May 12 '13 at 16:57

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Have you tried linear stability analysis of your equation?

I have been working on a a relatively simple nonlinear differential equation that cropped up during my phd studies, without any known closed form solution(I found a perturbation solution though). I tell you this because I have tried breaking the equation up and solving individual terms in a combination where I do know the solution to build up the target equation and I know that doesn't work, so I believe your approach is valiant if not flawed.

I will have a crack at this when I have time though.

Rob

Chinny84
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