1. ## ODE--y''+(y')^2=2e^(-y)

Could someone help me solve this?

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

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

2. Originally Posted by petition Edgecombe
Could someone help me solve this?

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

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

3. We haven't covered Bernoulli eqns yet, that's why I was stuck.