1. Find the Laplace transform of f(t) = t²e³t cos 2t 2. Find the inverse Laplace transform of F(s) = 7/(s² - 9) in expon
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1. Find the Laplace transform of f(t) = t²e³t cos 2t 2. Find the inverse Laplace transform of F(s) = 7/(s² - 9) in expon
1. Find the Laplace transform of f(t) = t²e³t cos 2t 2. Find the inverse Laplace transform of F(s) = 7/(s² - 9) in exponential terms.
Solve the following initial value problems using Laplace transform: 1. y" - 4y + 3y = 0, y(0) = 3, y'(0) = 7 2. y"+y = 3 cos 2t, y(0) = 0, y'(0) = 0 3. y" - 3y' + 2y = 4t + e³t, y(0) = 1, y'(0) = -1 4. x"(t) – 2x'(t) +2x(t) = 0, x(0) = 1, x'(0) = 1 5. y""" + 2y"+y = sint, y(0)=y'(0)=y" (0)=y""(0) = 0