Any analytical solutions to this second order nonlinear DE?

[pivoxa15]

Are there any analytical solutions to:

ay''+bx^2y+cxy+dy=0

where a,b,c,d are constants and y(x)

If so how would you go about it? Is there a website that teaches you how to solve these?

[HallsofIvy]

If by "analytical solutions" you mean "closed form solutions" then, in general no. The standard method of solution for such a function is to use an infinite series.

[arildno]

What you've written is a LINEAR ODE, BTW.

[mathwonk]

the usual technical meaning of the word "analytic" is a function defined by a power series, and in that sense , as Halls implied, the answer is yes.