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Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s y(0)...

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Mechanical Engineering

Use Laplace transformations to solve the following differentialequations:

dy(t)/dt + a y(t) = b; I.C.s y(0) = c

d2y(t)/dt2 + 6 dy(t)/dt + 9 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt =1

d2y(t)/dt2 + 4 dy(t)/dt + 8 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt =1

d2y(t)/dt2 + 2 dy(t)/dt + y(t) = 3e-2t; I.C.s y(0) = 1, dy(0)/dt= 1

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