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Consider the following initial value problem: x′′−3x′−40x=sin(2t),x(0)=4,x′(0)=3 Using X for the Laplace transform of x(t), i.e.,...

Consider the following initial value problem:

x′′−3x′−40x=sin(2t),x(0)=4,x′(0)=3

Using X for the Laplace transform of x(t), i.e., X=L{x(t)},, find the equation you get by taking the Laplace transform of the differential equation and solve for

X(s)=

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