The document provides additional exercises for solving non-homogenous differential equations. It includes two specific equations with their solutions: one simple equation resulting in y(x) = c1 + c2 e−3x, and another more complex equation solved using the variation of parameters method yielding y = yc + yp with specified components. These exercises aim to enhance understanding of differential equations.

1. Additional Exercises for ODE2 – Non-Homogenous

13. Try these:
1. Solve the differential equation (D.E) below
𝑑2
𝑦
𝑑𝑥
+ 3
𝑑𝑦
𝑑𝑥
= 0
Answer: 𝑦(𝑥) = 𝑐1 + 𝑐2 𝑒−3𝑥
2. Solve the D.E using variation of parameter method
𝑑2
𝑦
𝑑𝑥
− 4
𝑑𝑦
𝑑𝑥
+ 4𝑦 = (𝑥 + 1)𝑒2𝑥
Answer: y = 𝑦𝑐 + 𝑦𝑝 = 𝑐1𝑒2𝑥
+ 𝑐2𝑥 𝑒2𝑥
+
1
6
𝑥3
𝑒2𝑥
+
1
2
𝑥2
𝑒2𝑥