Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y″−12y′+36y=cos⁡(3t)−sin⁡(3t),y(0)= 5,y′(0)=1
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Y(s) =
Use the method of Laplace transforms to find a general solution to the differential equation below by assuming that a and b are arbitrary constants.
y" +12y' + 40y = 2, y(0) = a, y'(0)= b
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y(t) = .
(Type an exact answer in terms of e.)