I've got a nice differential equation I need to solve.

Question

kainui · Answer

$$y'' * y=a(y')^2$$ a is just a constant and y is just a function of x.

anonymous · Answer

Any "nice" techniques you know?

kainui · Answer

Not off the top of my head, it's been a while since I've really solved a differential equation. This is actually from separating:

$$u_{xx}u_{yy}=u_{xy}^2$$ with u(x,y)=X(x)Y(y)

but of course I've renamed the variables for simplicity... Any hints? I might just need a nudge in the right direction lol.

anonymous · Answer

lol wolfram is as cryptic as ever. There's an answer, but how to get it? http://www.wolframalpha.com/input/?i=%28y%27%27%29*y%3Dk*%28y%27%29%5E2

kainui · Answer

Actually that's wrong, it's simpler: http://www.wolframalpha.com/input/?i=y%27%27*y%3Dy%27%5E2 Yours assumed the constant k was really the variable of integration y(k). But I guess I don't believe that it has given me the real right answer... It seems wrong.

kainui · Answer

Wait I'm wrong too lol... http://www.wolframalpha.com/input/?i=y%27%27%28x%29*y%28x%29%3Day%27%28x%29%5E2