How do you find the general solution of a second order differential equation?

Steps:

1. Use the auxiliary equation on the equation given in the question
2. Solve the resulting equation
3. Identify the appropriate complementary function from the solutions
4. Determine an appropriate particular integral
5. Differentiate this equation twice
6. Sub in the particular integral and its differentials to the original equation in order to find the value of the constants in the particular integral
7. Find general solution by adding the complementary function and particular integral
8. Check!