This free online differential equations course teaches introductory to advanced methods for solving differential equations. The course consists of 53 tutorials which cover the material of a typical differential equations course at the university level. Tutorials 125 are complete and tutorials 2653 are currently under development.
The lessons build on each other so we recommend that you start at the top of the list and watch them all in order. 
First Order Differential Equations
1. What is a differential equation
2. How to classify differential equations 3. General solutions and initial value problems 4. How to solve a first order linear differential equation with integrating factors 5. First order linear differential equation example #1 6. First order linear differential equation example #2 7. How to solve separable differential equations 8. Separable differential equation example #1 9. Separable differential equation example #2 10. How to solve Bernoulli differential equations 11. Bernoulli differential equation example #1 12. Bernoulli differential equation example #2 13. How to solve exact differential equations 14. Exact differential equation example #1 15. Exact differential equation example #2 16. How to solve nonexact differential equations with an integrating factor 17. Nonexact differential equation example #1 18. Find m and n such that (x^n)(y^m) is an integrating factor 19. Euler's method for differential equations 20. Euler's method example #1 21. Euler's method example #2: calculating error of the approximation Second Order Differential Equations
22. Characteristic equation and general solution of a linear second order DE
23. Real distinct roots example 24. Real repeated roots example 25. Complex roots example 26. Fundamental solution set and wronskian explained 27. Reduction of order method 28. Reduction of order example 29. Method of undetermined coefficients method 30. Method of undetermined coefficients example 31. Variation of parameters method 32. Variation of parameters example 33. How to transform a differential equation to a system of linear equations 34. Find the solution of a differential equation using a linear system Laplace Transform35. What is a Laplace transform?
36. Laplace transform of f '(t) 37. Linear properties of Laplace transform 38. Laplace transform of 1 39. Laplace transform of t^n 40. Laplace transform of sin(at) 41. Laplace transform of cos(at) 42. Laplace transform of sinh(at) and cosh(at) 43. Laplace transform of (t^n)*(f(t)) 44. The first shifting theorem 45. The second shifting theorem 46. Inverse Laplace transforms part 1 47. Inverse Laplace transforms part 2 48. Laplace transforms of step functions 49. Using the Laplace transform to solve differential equations Power Series Solutions of Differential Equations
50. Some definitions regarding power series
51. How to find the interval of convergence for a power series 52. How to find the power series solution of a differential equation 
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