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10-5) Use the Laplace transform to solve: d^2y/dt^2+(w^2)y=sin wt, y(0)=y0, y'(0)=y1, Where w, y0, y1 are constants.

10-5)
Use the Laplace transform to solve:

d^2y/dt^2+(w^2)y=sin wt, y(0)=y0, y'(0)=y1,

Where w, y0, y1 are constants.
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Math-8100489.pdf

Solution
1. The given equation is
d2 y
+ ω 2 y = sin(ωt)
dt2
Taking laplace transform of the L.H.S and R.H.S we get,
´
s2 Y (s) − sy (0) − y (0) + ω 2 Y (s) = s2 ω
+ ω2 Therefore
Y(s) =...

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