Final answer:
To solve the second order differential equation x'' + 9x = u(t) using Laplace transform, apply the Laplace transform to both sides of the equation and rearrange to solve for X(s). Take the inverse Laplace transform to find x(t).
Step-by-step explanation:
To solve the second order differential equation x'' + 9x = u(t) using Laplace transform, we need to apply the Laplace transform to both sides of the equation. The Laplace transform of x'' is s^2X(s) - sx(0) - x'(0) and the Laplace transform of x is X(s). We also need to find the Laplace transform of the input function u(t).
After applying the Laplace transform, we can rearrange the equation to solve for X(s). Once we have X(s), we can find x(t) by taking the inverse Laplace transform.