I am trying to solve this equation with Frobenius method :
$(x^2-x)y''(x) + (1/3) y'(x) + xe^{(x-1)}y(x)=0$
I am trying to find the roots with : $r^2 + (P_0-1) + Q_0 = 0$
And, $P_0 = (1/0!)(1/3x)^{(0)}$ evaluated at $x=0$ but it gives me $1/0$!
I am able to find my $Q_0$ with : $Q_0 = (1/0!)((x-1)e^{(x-1)})^{(0)}$ evaluated at $x=0$ and it gives me $-1/e$.
How am I supposed to find my roots if $P_0 = 1/0$?
Thanks for your help!