1. differential equation hamzah asyrani sulaiman at www.asyrani.com www.asyrani.com

2. topic basic concept first order differential equation second order linear differential equation with constant coefficients the Laplace transform Fourier series

3. what is differential equation?

4. equation involving an unknown function and its derivatives

5. example

6. there are two types of differential equations (DE)

7. ordinary differential equation

14. Linear Differential Equations A linear differential equation is any differential equation that can be written in the following form *Important:- no products of the function, y(t), and its derivatives and neither the function or its derivatives occur to any power other than the first power

18. Got the idea? No? We try to look again

19. It has a form just like the previous one, we have:- y’(t), y(t) It has y’’(t), and y(t) It has y’’’(t), y’(t), and y(t)

22. Solution to a differential equation

23. example

24. Solution We’ll need the first and second derivatives to do this

25. Solution Plug these as well as the function into the differential equation.

26. Solution

27. To see why recall that In this form, it is clear that we’ll need to avoid x=0 at the least as this would give division by zero. And then, x > 0 (forever).

28. Initial Value Problem Initial condition(s) is a condition or set of conditions that help you to solve the differential equation problem

29. Initial Condition(s) example

30. Interval of Validity

31. General Solution of DE The general solution to a differential equation is the most general form that the solution can take and doesn’t take any initial conditions into account. Just a regular DE

32. Actual Solution of DE What is the actual solution to the following IVP?

33. Actual Solution of DE

34. Implicit/Explicit Solution

35. Explicit function

36. Implicit function

37. Homogeneous Function

38. How to detect homogeneous or not

39. Homogenity