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Solving Differential Equations using Laplace Transform
a) y\" - y' -2y = 0
y(0) = 1, y'(0) = 0
answer: y = 1/3e^2t + 2/3e^-t
b) y\" + y = sin2t
y(0) = 2, y'(0) = 1
answer: y(t) = 2cost + 5/3 sint - 1/3sin2t
c) y^4 - y = 0
y(0) = 0, y'(0) = 1, y\"(0) = 0, y'''(0) = 0
answer y(t) = (sinht + sint)/2
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