Consider the initial value problem y\" + 16y = 32t, y(0) = 5, y\' (0) = 4.| a. T

Question

Consider the initial value problem y" + 16y = 32t, y(0) = 5, y' (0) = 4.| a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t)| by Y(s)|. Do not move any terms from one side of the equation to the other (until you get to part (b) below). =| b. Solve your equation for Y(s)|. Y(s) = L{y(t)} =| c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t)|. y(t) =|

Explanation / Answer

Given that

changing mixed fraction into single fraction

1.(3/8) = 1+ (3/8)= 11/8

We know that

Reciprocal of fraction a/b = b/a

Therefore ,

Reciprocal of 11/8 = 8/11

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