Consider the following initial value problem. y" + 8y' + 25y = 8(t – x) + 8(t – 7x), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -TS e -7as + (s + 8) +e L{y} = (s+4)² + 3² Use the Laplace transform to solve the given initial-value problem. 4-4'e sin (31) x 1 -4(n-t) 2. 3 'sin 3(1 – a) × ) · a(e – a) + (| 4t e-"cos(3t) x y(t) = t- · Ut -| 77

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