ODE--y''+(y')^2=2e^(-y)

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October 15th 2008, 02:47 AM
petition Edgecombe

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.
October 15th 2008, 04:51 AM
mr fantastic

Quote:

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.
October 15th 2008, 08:03 PM
petition Edgecombe

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

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