Use the Laplace transform to solve the following initial value problem: y" - 1y - 30y = 0 y(0) = −4, y'(0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) Y(s) = Now by inverting the transform, find y(t) = = A s+a + where a < b B 8+6

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Q: 11

A: Step 1: Step 2: Step 3: Step 4: