# Thread: Euler Cauchy 3rd Order Linear DE

1. ## Euler Cauchy 3rd Order Linear DE

$\displaystyle x^3y'''-x^2y''+2xy'-2y=0$

That is the Given ODE, am not sure how to find the characterstic polynomial please if anyone could guide me on how to do that? my guess from reading and checking websites i got.

$\displaystyle m^3-4m^2+5m-2=0$

2. Originally Posted by zangestu888
$\displaystyle x^3y'''-x^2y''+2xy'-2y=0$

That is the Given ODE, am not sure how to find the characterstic polynomial please if anyone could guide me on how to do that? my guess from reading and checking websites i got.

$\displaystyle m^3-4m^2+5m-2=0$
Use a trial solution $\displaystyle y=x^m$ which then gives:

$\displaystyle m(m-1)(m-2)-m(m-1)+2m-2=0$