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Differential Equations II

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Lecture 20: Repeated roots of the characteristic equation

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Lecture Details :

What happens when the characteristic equation only has 1 repeated root?

Course Description :

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus course before starting here.

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  1. Introduction to differential equations
  2. Separable Differential Equations
  3. Separable differential equations 2
  4. Exact Equations Intuition 1 (proofy)
  5. Exact Equations Intuition 2 (proofy)
  6. Exact Equations Example 1
  7. Exact Equations Example 2
  8. Exact Equations Example 3
  9. Integrating factors 1
  10. Integrating factors 2
  11. First order homegenous equations
  12. First order homogenous equations 2
  13. 2nd Order Linear Homogeneous Differential Equations 1
  14. 2nd Order Linear Homogeneous Differential Equations 2
  15. 2nd Order Linear Homogeneous Differential Equations 3
  16. 2nd Order Linear Homogeneous Differential Equations 4
  17. Complex roots of the characteristic equations 1
  18. Complex roots of the characteristic equations 2
  19. Complex roots of the characteristic equations 3
  20. Repeated roots of the characteristic equation
  21. Repeated roots of the characterisitic equations part 2
  22. Undetermined Coefficients 1
  23. Undetermined Coefficients 2
  24. Undetermined Coefficients 3
  25. Undetermined Coefficients 4
  26. Laplace Transform 1
  27. Laplace Transform 2
  28. Laplace Transform 3 (L{sin(at)})
  29. Laplace Transform 4
  30. Laplace Transform 5
  31. Laplace Transform 6
  32. Laplace Transform to solve an equation
  33. Laplace Transform solves an equation 2
  34. More Laplace Transform tools
  35. Using the Laplace Transform to solve a nonhomogenous eq
  36. Laplace Transform of : L{t}
  37. Laplace Transform of t^n: L{t^n}
  38. Laplace Transform of the Unit Step Function
  39. Inverse Laplace Examples
  40. Laplace/Step Function Differential Equation
  41. Dirac Delta Function
  42. Laplace Transform of the Dirac Delta Function
  43. Introduction to the Convolution
  44. The Convolution and the Laplace Transform
  45. Using the Convolution Theorem to Solve an Initial Value Prob