Hello tutors, may I please get your help solving this differential equation. Use the given general solution to find a solution of the differential equation having the given initial condition. Sketch the solution, the initial condition, & discuss the solution's interval of existence.

Problem 1: y' + 4y = cos(t), y(t) = (4/17)cos(t) + (1/17)sin(t) + Ce^-4t, y (0) = 1

Problem 2: ty + (t+1)y = 2te^t, y(t)=e^t(t+C/t), y(1) = 1/e

Thank you!