Solve the following initial value problem using Laplace transform: d²y dt² 19 dy where - dy +60y = g(t), y (0) = -1/2, t-o= 11, 2 0≤t <3 6 3 ≤t g (t) Let Y (s) be the Laplace transform of the solution y(t). Then evaluate Y(-1/2) y(-1/2). Y(-1/2) y (-1/2) =

Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

Q: Find the Laplace transform of f(t) = te-5t.

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).