(21 pts) Solve the IVP:
y' - y = 2te2t, y(0) = 1
This is a liner equation of the first order. There's an obvious integrating factor: e-t. Multiply by e-t to get: (ye-t)' = 2tet. Integrate both sides:
All that remains is to satisy the initial condition. Plug in t = 0: y(0) = -2 + C = 1. C = 3.