From the definition of the laplace transform, compute L (f (t)) for 1. f(t) = cost...

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From the definition of the laplace transform, compute L (f (t)) for 1. f(t) = cos²t 2. f(t) = e2t sin t Solve the following differential equation with the given initial conditions using the Laplace Transformation method 3. y" + y' – 6y = 5e2t , y(0) = y'(0) = 0 4. y" – y' - 6y = e3t , y(0) = -1 , y'(0) = 0 Determine 5. L-1 3s2 6. L-1 (s+2)(s-4)(2s+1), 7. L- +2s+s/ s-1 8. L-1 (s+1)2 From the definition of the laplace transform, compute L (f (t)) for 1. f(t) = cos²t 2. f(t) = e2t sin t Solve the following differential equation with the given initial conditions using the Laplace Transformation method 3. y" + y' – 6y = 5e2t , y(0) = y'(0) = 0 4. y" – y' - 6y = e3t , y(0) = -1 , y'(0) = 0 Determine 5. L-1 3s2 6. L-1 (s+2)(s-4)(2s+1), 7. L- +2s+s/ s-1 8. L-1 (s+1)2