NAME: 1. Find the Laplace transforms of (a) sin 3t+ 6 cos 5t|-75 ++3etcost, and (b)...

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NAME: 1. Find the Laplace transforms of (a) sin 3t+ 6 cos 5t|-75 +€−³+√3e³tcost, and (b) te sin √³t - 6 + e² sin 5t. Ans. 2. Find the inverse Laplace transform of the functions: 8³-38+5 8(8+1)(8-2)(a − 1) ' Ans. Ans. (a) 3. Solve the following equation using the Laplace transform method y" + 2y' + y = 0, y(0) = 1, y'(0) = 1. Ans. 4. Solve the following problem using the Laplace transform method y" + y + y = sint, y(0) = 1, y(0) = 0. (b) y" - ²-3 8(8²+2) 5. (a) Start from the definition of the Laplace transform of sin bt and deduce the Laplace transform of t cos bt (differentiation is involved). (b) Solve the equation - 4y = t cos 2t, using the Laplace transform method. Ans. y(0) = 1, y'(0) = 2 NAME: 1. Find the Laplace transforms of (a) sin 3t+ 6 cos 5t|-75 +€−³+√3e³tcost, and (b) te sin √³t - 6 + e² sin 5t. Ans. 2. Find the inverse Laplace transform of the functions: 8³-38+5 8(8+1)(8-2)(a − 1) ' Ans. Ans. (a) 3. Solve the following equation using the Laplace transform method y" + 2y' + y = 0, y(0) = 1, y'(0) = 1. Ans. 4. Solve the following problem using the Laplace transform method y" + y + y = sint, y(0) = 1, y(0) = 0. (b) y" - ²-3 8(8²+2) 5. (a) Start from the definition of the Laplace transform of sin bt and deduce the Laplace transform of t cos bt (differentiation is involved). (b) Solve the equation - 4y = t cos 2t, using the Laplace transform method. Ans. y(0) = 1, y'(0) = 2