Workshop Quiz Week 12, Trimester 2, 2022 1. Solve the differential equation 1+ 3y = 12x' + 5x + 8 with initial condition r = 0, y = 5. d.x You may find the following steps helpful when solving the differential equation. However, you are not required to complete the following steps. You are only required to solve the differential equation. (a) Start by solving the homogeneous differential equation dy + 3y = 0. Hint: Do not apply the initial condition at this stage. (b) Guess the form of the particular solution. Hint: The RHS is a quadratic. (c) Find the value of all unknown constants in your particular solution by substituting it into the original equation. Hint: By considering the coefficients of x2 and x, as well as the constant term, you will have three equations to solve for the three unknowns. (d) Combine the homogeneous and particular solutions to obtain the general solution to the differential equation. Hint: y = yu + yp (e) Use the initial condition to find the final solution to the differential equation