$(10$ points$)$ Solve the following ODE with initial conditions by separation of wariables. Check your answer by taking the appropriate derivative$($s$)$ of the solution $($substitute for $\frac{ey}{er}$ and the solution $y$ in the ODE and show that it results in an identity$).$

$\frac{dy}{dx}+8xy=16x,y(0)=3$