Please help me solve a differential equation.

Question

anonymous · Answer

what equation

anonymous · Answer

$$\frac{ d^2 \phi }{ d \eta^2 }+2 \eta \frac{d \phi}{d \eta}=0$$

anonymous · Answer

This is a second-order diff. eq. with a variable coefficient. I think it may be solvable analytically using Cauchy-Euler method but I don't know how it goes exactly.

anonymous · Answer

I know that I can make a substitution:

$$\Psi = \frac{d \phi}{d \eta}$$

to get:

$$\frac{d \Psi}{d \eta}+2 \eta \Psi=0$$

which is a separable DE. But I need to be able to solve it directly

anonymous · Answer

Anybody?

anonymous · Answer

a shiny medal in it for whom-so-ever is smart enough.

anonymous · Answer

Oh c'mon guys; I know at least a handful of you got past Calculus...

anonymous · Answer

Anybody remember Cauchy-Euler method; anybody have their Diff. Eq. textbook handy. Just tell me how it goes cause I don't have mine available right now.

anonymous · Answer

I know the solution involves the error function somehow...