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)+5y=0), (y(0)=1), (y^(\ ')(0)=0) :}`

Using the "Solve exact" tool gives us: `y(t)=e^[-t] cos\ 2t + 1/2e^[-t] sin\ 2t`

Note: In SNB , we can also do "Laplace solution". It gives the same answer.

The graph of what we have found: