$4$ During the solution of a linear differential equation for $x(t),$ with the initial condition $x(2)=15,$ the following step has been reached:

$\frac{d}{dt}(x(t)e^t)=cos(t^4)$

Finish the solution of the problem. $($Hint: you may need to leave an unevaluated definite integral in your solution.$)$