Error function as a solution to a second order ode

[Juggler123]

Hi I need to find the solution of

d^2y/dx^2 + 2x(dy/dx) = 0

I've solved it in Maple and get that

y=a*erf(x)+b

but I have no idea how to arrive at this answer!
Any help would be great, thanks.

 

[jackmell]

Start by letting u=y' then you have:

$$u'+2xu=0$$

which I'm sure you know how to solve, then when you get the solution for u, then integrate it once more to get y.

 

[Juggler123]

Simple! Thanks.