Question: Use the laplace transform to solve the initial value problem (1 point) Consider the following initial value problem: y 6y' 16y = sin(4z) y(0) =

Use the laplace transform to solve the initial value problem

$Consider the following initial value problem: y\" 6y' 16y = sin(4z) y(0)$ = 2, M) = 4 Using Y for the Laplace transform of

(1 point) Consider the following initial value problem: y\" 6y' 16y = sin(4z) y(0) = 2, M) = 4 Using Y for the Laplace transform of y(t), i.e., Y = {y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) = C] (1 point) Consider the following initial value problem: y" - 5y' - 14y = sin(9t) y(0) = -2, y' (0) = 7 Using Y for the Laplace transform of y(t), i.e., Y = [ly(t) }, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =(1 point) Use the Laplace transform to solve the following initial value problem: " +4y' - 21y = 0 y(0) = -3, y' (0) = -3 a. First, using Y for the Laplace transform of y(t), i.e., Y = [ly(t) }, find the equation you get by taking the Laplace transform of the differential equation = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = A sta + B sth Where a

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