1. 1Chapter 2

2. 2

3. Example 3Chapter 2

4. 4

5. EXAMPLE 5Chapter 2

6. Solution 6Chapter 2

7. 7

8. 8

9. 9 Method for solving First Order Differential Equations Differential Equations Method for solving First Order Differential Equations Differential Equations

10. Methods Variable Separable Reducible to variable separable Exact Differential Equation Integrating Factor

11. Separable Variable x is independent variable and y is dependent variable or are separable forms of the differential equation or General solution can be solved by directly integrating both the sides + c Where c is constant of integration 11 Chapter 2 DO YOU REMEMBER INTEGRATION FORMULA? Variable Separable Differential Equation Chapter 2

12. Separation of Variables Definition A differential equation of the type y’ = f(x)g(y) is separable. Example Separable differential equations can often be solved with direct integration. This may lead to an equation which defines the solution implicitly rather than directly. Variable Separable Differential Equation Chapter 2

13. EXAMPLE: 13Chapter 2 Variable Separable Differential Equation Chapter 2

14. EXAMPLE: 14Chapter 2 Variable Separable Differential Equation Chapter 2

15. To find the particular solution, we apply the given initial condition, when x =1, y = 3 is solution of initial value problem 15Chapter 2 Variable Separable Differential Equation Chapter 2

16. 16Chapter 2 Variable Separable Differential Equation Chapter 2

17. 17Chapter 2 Variable Separable Differential Equation Chapter 2

18. Chapter 218 Note1: If we have Integrating by parts Note.2. If we have Integrating by parts Note.3. If we have

19. Chapter 219 Variable Separable Differential Equation Chapter 2

20. Chapter 220

21. Chapter 221