(a) Do not solve the following differential equations. State the difference between homogeneous second order differential equation and non-homogeneous second order differential equation. i. ii. The...

Extracted text: (a) Do not solve the following differential equations. State the difference between homogeneous second order differential equation and non-homogeneous second order differential equation. i. ii. The auxiliary equation of a second order differential equation, d?y dy +b + cy = 0 dx? dr has 2 real unequal roots, m = -4 and m = 5. Write the general solution for this equation. ii. Write the trial solution of the particular integral for the following equation, d?y dæ? + 2y = 3e" cos(2x) iv. Can y = Csin(3x)+ Dcos(3x) be the trial solution for the following equation. d²y + 9y = 6cos(3x) da? If your answer is no, explain your answer and suggest a new trial solution.