If x(t) satisfies the initial value problem x′′ + 2px′ + (p2 + 1)x = δ(t − 2π), x(0) = 0, x′(0) = v0. then show that x(t

[answerhappygod]

If x(t) satisfies the initial value problem
x′′ + 2px′ + (p2 + 1)x = δ(t − 2π), x(0) = 0, x′(0) = v0.
then show that x(t) = (v0 + e^(2πp)u(t − 2π))e^(−pt) sin t.
Here δ denotes the Dirac delta function and u denotes theHeaviside step function as in the textbook.