Third order differential equation with variable coefficients I am wondering if there were known methods for solving this type of differential equations ? 
$$x^2y'''+3xy''+2xy'+2y=0$$
Thank you in advance

You can reduce the order of the DE:
$$x^2y'''+3xy''+2xy'+2y=0$$
$$(x^2y'')'+(xy')'-y'+2(xy)'=0$$
Integrate:
$$x^2y''+xy'+(2x-1)y=C_1$$
Now it's a second order DE. Then use reduction of order or series solution.
