Consider the following initial value problem. у" + 8y' + 25у %3D 6(t — л) + 6(t — 7л), у(0) %3D 1, у'(0) = 0 - Find the Laplace transform of the differential equation. (Write your answer as a function...

Extracted text: Consider the following initial value problem. у" + 8y' + 25у %3D 6(t — л) + 6(t — 7л), у(0) %3D 1, у'(0) = 0 - Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -TS -7Ts + e + (s + 8) e L{y} (s + 4)² + 32 Use the Laplace transform to solve the given initial-value problem. 4 -4t H )+( že 1,-4(1-1)sin 3(t– n) | × ). a(e - -) + ( e Hcos(3t) × 'e sin( 3t) x -4t. y(t) t - T t - 3