The solution of a certain differential equation is of the form $$y(t) = a \exp(5 t) + b \exp(7 t),$$ where $a$ and $b$ are constants.
The solution has initial conditions $y(0) = 1$ and $y'(0) = 4 .$
Find the solution by using the initial conditions to get linear equations for $a$ and $b.$

$y(t)=$