(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find an approximate oscillating soution of y'' = (y-x)^2 - exp(2*(y-x))

where y=y(x), y'' denotes second deriviate

2. Relevant equations

y'' = (y-x)^2 - exp(2*(y-x))

3. The attempt at a solution

I try to change a variable with p = y-x, so

dy/dx = dp/dx+1

y'' = p''

The original equation becomes p'' = p^2 - exp(2p)

when p^2 close to exp(2p) or p close to exp(p), we have p'' -> 0, i.e. p -> ax+b

I think the approximate solution is p = ax + b, but it turns out to be not. Does anyone give me some hint to find out the approximate oscillating solution? Thanks in advance

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# Homework Help: An approximation of a differential equation

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