Question

This question concerns the second-order differential equation (ODE) below, subjectto initial conditions x = D and * = 0 when t = 0:dxdt \frac{d^{2} x}{d t^{2}}-A \frac{d x}{d t}-B x=C

(i)Determine the complementary function for the associated homogeneous ODE. (ii)Use undetermined coefficients to find the particular solution for the full equation. (iii) Combine the solutions from (i) and (ii) with the initial conditions to find the general solution to the ODE.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5