Using Scientific Notebook, we can solve it in one step.

We set up a matrix with the differential equation and initial conditions:

`{: ( (d^2y)/(dt^2) -2(dy)/(dt)+y=e^t), (y(0)=-2), (y^(\ ')(0)=-3) :}`

Exact solution is:

`y(t)=1/2 t^2 e^t - 2e^t - e^t t`