> 
> Write the general solution 
>  for $ (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? It's a homework question so i guess (i / you) can solve it.

Euler ODE doesn't work here .

> 
> Can you help me with the solutions i got 4 solutions : ( after solving Euler equation and moving to $ v''' $ .
> 
> 
> 

$y'(x) = \{ e^{-x} ,~ \frac{x^3}{3}e^{-x} ,~ \frac{x^2}{2}e^{-x} \}$ or any linear combination of those, **uniqueness theorem doesn't apply here near $x=0$**