The solution of a certain differential equation is of the form
$$y(t) = a \exp(3t) + b \exp(7t),$$
where a and b are constants.
The solution has initial conditions $$y(0) = 3$$ and $$y'(0) = 5.$$
Find the solution by using the initial conditions to get linear equations for a
and b.
$$y(t) =$$
Note: the notation $$\exp(t)$$ means $$e^t$$ (e to the power of t).
