1. Use the method of Laplace transforms to solve the IVP with a piecewise-defined right-hand side and simplify your answer as much as possible: y"+5y'+4y=30e-2tu(t -1n2),y(0)=0,y'(0)=0
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The Laplace transform of y'' is s^2Y(s) - sy(0) - y'(0) The Laplace transform of y' is sY(s) - y(0) So, the Laplace transform of the differential equation becomes: s^2Y(s) - sy(0) - y'(0) + 5(sY(s) - y(0)) + 4Y(s) = 30e^(-2t)U(t) - 30e^(-2t)U(t-2) Show more…
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