(Solved): Find the general solution, \( y(t) \), which solves the problem below, by the method of integratin ...

Find the general solution, \( y(t) \), which solves the problem below, by the method of integrating factors. \[ 5 t \frac{d y}{d t}+y=t^{7}, \quad t>0 \] Put the problem in standard form. Then find the integrating factor, \( \mu(t)=t^{\frac{1}{5}} \), and finally find \( y(t)= \) (use \( C \) as the unkown constant.)