I have been tasked with solving the following differential equation:
$$y'(t)+7\sin(t)y(t)=(te^{\cos(t)})^7$$
I recognize (I think?) that this is an equation of the type:
$$y'(t)+p(t)y(t)=q(t)$$
which has the solution:
$$y(t)=e^{-P(t)}\int e^{P(t)}q(t)dt$$
However, I just can't figure out which function goes where in the solutioon formula. Can anyone help me?
You can define
$z(t):=(e^{-cos(t)})^7y(t)$
and you can observe that $z(t)$ verify the equality
$z’(t)=t^7$