
Robert J. answered 07/03/13
Certified High School AP Calculus and Physics Teacher
Use the solution formula for the first order linear differential equation, as I showed you here many times recently,
y = e^(t)[∫e^(-t)(1+3sin(t)) dt + c] = -(1/2)(3sin(t) + 3cos(t) + 2) + ce^(t), after doing integration by parts twice.
Since lim{t->oo} y is finite, c = 0.
So, y(0) = -(1/2)(3+2) = -5/2 <==Answer
Robert J.
y1 = (3/2)(sint - cost) - 1 <==You had a typo here.
y(0) = -5/2, the same answer as I got.
07/03/13