$ (x^2) y”” + (3x^2-2x)y”’ + (3x^2-4x+2)y” +(x^2-2x+2)y’ = 0 $

i tried to **Guess** a solution and use the fact that i can decrease the ODE to less power ( to $ y”’$ ) by using the Wronskian .

i Guessed that $ e^{-x} $ is a solution . is it the way we solve this kind of equations ? its homework question so i guess i can solve it.

euler ODE doesn’t work here .