Please show the solutions to how it came to the answers using MUC. Thank you.

Solve the following differential equations using MUC. 1. y"ty=ex Ans: y = C cos x + C sinx + 2. y" - 4y = 2+3x - x- Ans: y = Cle* + C,e-2x X + 3. y" - 9y = ex Ans: y = Cle3* + Cze-3x + - xe3X 6 4. y" + 16y = cos 4x Ans: y = C cos 4x + C sin 4x + = x sin 4x 5. y"+ 4y = sin x + 3 cos x Ans: y = C + C, cos 2x + C, sin 2x + sin x - = cosx