I have been trying to solve the differential equation $t y''(t) +2 y'(t) - ty(t)=0$ through the Frobenius method. WolframAlpha says the solution should be $ y(t) = c\_1 \frac{e^{-t}}{t} + c\_2\frac{e^t}{t}$. I got that $r=0 \lor r=-1$. For $r=0$, we get that $a\_{n+1}=\frac{a\_{n-1}}{(n+1)(n+2)}$, so $a\_{2k}=\frac{1}{(2k+1)!}$, but this will not get me the correct solution. Could anyone try to solve it and tell me where I went wrong?