I am trying to solve this problem, but am having some trouble.
The ODE $u''=\cfrac{u'}t - 4t^2u$ has the solution $u(t)=\sin(t^2)+\cos(t^2)$.
I want to plot the exact solution over the interval $[1,20]$. Can someone help me figure out this exact solution and how to go about solving it?
Thanks!