Verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given inhomogeneous equation:
\begin{equation*}
(1-t)y''+ty'-y=2(t-1)^{2}e^{-t}, 0<t<1;
\end{equation*}
\begin{equation*}
y_1(t)=e^{t}, y_2(t)=t.
\end{equation*}
Here is my solution:
