I need help solving $y'(t)+7\sin(t)y(t)=(te^{\cos(t)})^7$ (differential equation) I need help solving the following differential equation: $$y'(t)+7\sin(t)y(t)=(te^{\cos(t)})^7$$ Can anyone push me in the right direction?

$$y'(t)+7\sin(t)y(t)=(te^{\cos(t)})^7$$ $$y'(t)e^{-7\cos(t)}+7\sin(t)y(t)e^{-7\cos(t)}=t^7$$

Rewrite it as $$\implies (y(t)e^{-7\cos(t)})'=t^7$$ And integrate...