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3. Find the Laplace transforms of the following functions u2022 f(t) = t cos t u2022 g(t) = te^{-3t} + sin^2 t 4. (20 points) Find the Inverse Laplace Transform of the following functions u2022 F(s) = frac{1}{s^2(s - 2)} u2022 G(s) = frac{s}{s^2 + 4s + 13} 5. (20 points) Solve the initial value problem using the Laplace Transform frac{d^2y}{dt^2} + 2frac{dy}{dt} + y = te^{-2t}, y(0) = 1, y'(0) = 0,

          3. Find the Laplace transforms of the following functions
u2022 f(t) = t cos t
u2022 g(t) = te^{-3t} + sin^2 t

4. (20 points) Find the Inverse Laplace Transform of the following functions
u2022 F(s) = frac{1}{s^2(s - 2)}
u2022 G(s) = frac{s}{s^2 + 4s + 13}

5. (20 points) Solve the initial value problem using the Laplace Transform
frac{d^2y}{dt^2} + 2frac{dy}{dt} + y = te^{-2t}, y(0) = 1, y'(0) = 0,

$3. Find the Laplace transforms of the following functions u2022 f(t) = t cos t u2022 g(t) = te^-3t + sin^2 t 4. (20 points) Find the Inverse Laplace Transform of the following functions u2022 F(s) = frac1s^2(s - 2) u2022 G(s) = fracss^2 + 4s + 13 5. (20 points) Solve the initial value problem using the Laplace Transform fracd^2ydt^2 + 2fracdydt + y = te^-2t, y(0) = 1, y'(0) = 0,$

Added by Ver-Nica A.

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