One way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. This video is an example of the process where the roots are complex.

1. Fundamental Set of Solutions
2. Solving Differential Equations: Two Distinct Real Roots
3. Transforming Systems ODE's and Checking Solutions
4. Solving ODE's with Complex Eigen Values
5. Solving Systems with Repeated Eigen Values
6. Test For Stability of the Origin
7. Solving Separable DE: Example I
8. Solving Separable DE: Example II
9. Solve Separable DEs Using Substitution
10. Introduction to Differential Equations
11. Check Homogeneous DE y=vx
12. Solving First Order Homogeneous DE: Separable First Order DE Using y=vx (Part I)
13. Solving First Order Homogeneous DE: Separable First Order DE Using y=vx (Part II)
14. Solving First Order Homogeneous DE: Translation and Substitution (Part III)
15. Derivation a General Solution and Integrating Factor for a Linear Differential Equation
16. Linear Differental Equations: Example I
17. Linear Differential Equations: Example II
18. Using Differential Operators
19. Solving Linear DE's with Two Distinct Real Roots
20. Solving Linear DE's with Repeated Real Roots
21. Solving Linear DE's with Complex Roots
22. Fundamental Solution Set for Linear DE's
23. Factoring Operators
24. Annihilator Method I
25. Writing a Differential Equation as a System
26. Existence and Uniqueness Linear D.E.'s
27. Linear Combination and General Solutions to Linear D.E.'s
28. Runge-Kutta Method
29. The Wronskian and a Test for Independence
30. Euler Method