Use Laplace transforms to compute the solution to the following differential equation dy (a) dt dy...

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Use Laplace transforms to compute the solution to the following differential equation dy (a) dt dy (b) - 2y = u(t), y(0) = = 1 dt dy + 10y = 4 sin(2t)u(t), y(0) = 1 dt dy dt (c) (d) +10y = 8e-10u(t), y(0) = 0 dy +8y= u(t), y(0) = 0, y(0) = 1 dt dy (f) +6- +9y= sin(2t)u(t), y(0) = 0, y(0) = 0 dr² dt (e) + 2y = u(t), y(0) = 0 dt² +6- Use Laplace transforms to compute the solution to the following differential equation dy (a) dt dy (b) - 2y = u(t), y(0) = = 1 dt dy + 10y = 4 sin(2t)u(t), y(0) = 1 dt dy dt (c) (d) +10y = 8e-10u(t), y(0) = 0 dy +8y= u(t), y(0) = 0, y(0) = 1 dt dy (f) +6- +9y= sin(2t)u(t), y(0) = 0, y(0) = 0 dr² dt (e) + 2y = u(t), y(0) = 0 dt² +6-