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

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

`(dy)/(dt)+y=sin 3t`

`y(0)=0`

We then solve it to give the exact solution: `y(t)=-3/10 cos\ 3t+1/10 sin\ 3t+3/10e^(-t)`

This is the graph of our solution: