Q8. (10 marks) Using Euler's method with a step size of h = 0.1, find the value of X(1.3) for the initial-value problem dx/dt = z(1) = 2F + JP. Note that the calculations incurred in this Question 8 must be with at least five decimal place accuracy.
Q9. (10 marks) Find the general solution of the following differential equation:
f''(t) + 4x = 3t + 2
Q10.* (10 marks) Figure 1 below depicts an RLC circuit in which R, L, and C are in series. The RLC circuit is with R = 22Ω, L = 0.2H, C = 0.005F. Moreover, denote by i(t) the current inside the circuit. The circuit is connected to a source of voltage E(t) = 200sin(400t). The RLC circuit in Figure 1 is modeled by the following ODE:
di(t)/dt + R/L * i(t) + 1/(LC) * ∫i(t)dt = E(t)
Find the current i(t) in the RLC circuit. Assume that the initial conditions are zero, i.e., i(0) = 0 and d/dt(i(0)) = 0.