having trouble with this problem

Problem 4 Given the ODE cos(t) - y\"(t) + (sin(t) 4cos(t)) - y'(t) + (4 cos(t) 2 sin(t)) - y(t) = 62* cos2(t) (a) If further given initial condition y(0) = 1, y'(0) = 0, explain why there is a unique solution y. What does the existence and uniqueness theorem say about the domain of y? (b) If you are told that y1 = 62* is a solution to cos(t) - y"(t) + (sin(t) 4cos(t)) -y'(t) + (4cos(t) 2sin(t)) - y(t) = 0 nd the general solution to cos(t) - y\"(t) + (sin(t) 4cos(t)) - y'(t) + (4 cos(t) 2 sin(t)) - y(t) = 62' cos2(t) (c) Use your solution in Part (b) to nd the solution to the initial value problem in Part (a), then decide its actual domain