I need help solving this differential equation
$$y'(t)+7\sin(t)y(t)=(te^{\cos(t)})^{7}$$
What I've tried:
$$\implies e^{-\cos(t)}y'(t)+e^{-7\cos(t)}7\sin(t)y(t)=t^{7}$$ $$\implies (y(t)e^{-7\cos(t)})'=t^7$$ $$\implies y(t)e^{-7\cos(t)}=\int t^7 dt = \frac{t^8}{8}+c$$ $$\implies y(t)=\frac{e^{7\cos(t)}t^8}{8}+c$$
However, when I use Maple's dsolve I get a different result. Can anyone see where I've gone wrong?
You forgot to multiply the constant C by $\exp(7cos(t))$ on your result.