find the general solution(ode) Isn't the general solution yh + yp? What am I doing wrong? Got everything else correct, but stuck on question d.
HINT

To start with, rearrange the given ODE in the following manner

\begin{align*}
y^{\prime\prime} - 2y^{\prime} + y = (y^{\prime} - y)^{\prime} - (y^{\prime} - y)
\end{align*}

Then make the substitution $u = y^{\prime} - y$, which reduces the problem to solving a first order ODE twice.
The given answer is not correct.

Your $$y_h = c_1e^t+c_2te^t$$ is correct but the $y_p$ is not .
To find $y_p$ they used the method of variation of parameters as explained in the solution but they have their $y_p$  incorrect. The correct $y_p=-t^2e^t$ does not need the $c_1$ and $c_2$ but it uses $u_1e^t+u_2te^t$ where $u_1$  and $u_2$ are  found by the integrals.

The correct answer is $$y=  c_1e^t+c_2te^t -t^2e^t $$