Question: Please write on paper and explain Problems 1. Use the method of Laplace transforms to solve the IVP: y + 10y' + 30y = 0,

Please write on paper and explain

Problems 1. Use the method of Laplace transforms to solve the IVP: y" + 10y' + 30y = 0, y(0) = 6, y'(0) = -8. 2. Use the method of Laplace transforms to solve the IVP: y" - 3y' - 10y = 30et, y(0) = 0, y'(0) = 3. 3. Consider the following piecewise-defined function f(t) on [0, co): 0, 0 In4 (a) Sketch the graph of f (t). (b) Rewrite f(t) as a linear combination of multiples of shifted Heaviside functions u(t - a), where the coefficients are functions of t. (c) Calculate the Laplace transform of f (t)

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