Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1, у'(0) 3D о Find the Laplace transform of the differential equation. (Write your answer as a function...

Extracted text: Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1, у'(0) 3D о Find the Laplace transform of the differential equation. (Write your answer as a function of s.) L{y} = Use the Laplace transform to solve the given initial-value problem. cos 3t + sin( 31) x )+ ( je 1,-4(1—т) sin 3(t – n) | × y(t) t - + 1,-4(+-7п), sin 3(t – 7n) * ) U t - t – 7n