Using the Laplace transform method, solve for t≥ 0 the following differential equation: ď²x dx +5a- +68x = 0, dt dt² subject to x(0) = xo and (0) = o. In the given ODE, a and are scalar coefficients. Also, To and io are values of the initial conditions. Moreover, it is known that r(t) = 2e-¹/2 (cos(t) - 24 sin(t)) is a solution of ODE+ a + x = 0.
