Could someone help me solve this?

$\displaystyle y''+(y')^2=2e^{-y}$

So far I've got $\displaystyle v\frac{dv}{dy}+v^2=2e^{-y}$ with $\displaystyle v=y'$, which I also cannot solve.

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- Oct 15th 2008, 02:47 AMpetition EdgecombeODE--y''+(y')^2=2e^(-y)
Could someone help me solve this?

$\displaystyle y''+(y')^2=2e^{-y}$

So far I've got $\displaystyle v\frac{dv}{dy}+v^2=2e^{-y}$ with $\displaystyle v=y'$, which I also cannot solve. - Oct 15th 2008, 04:51 AMmr fantastic
Divide by v and re-arrange to recognise that it's a Bernoulli DE: Bernoulli differential equation - Wikipedia, the free encyclopedia

So make the substitution w = v^2. - Oct 15th 2008, 08:03 PMpetition Edgecombe
We haven't covered Bernoulli eqns yet, that's why I was stuck.