1. Differential Equations
Any equation containing a derivative is called a
differential equation.

2. Differential Equations
A function which satisfies the equation is called
a solution to the differential equation.

3. Differential Equations.
The general solution is a family of curves. Each member is a particular solution

4. Differential Equations
The order of the differential equation is the order
of the highest derivative involved.
These are examples of FIRST ORDER differential equations

5. Differential Equations
The order of the differential equation is the order
of the highest derivative involved.
These are examples of SECOND ORDER differential equations

6. 3 Types of Differential Equations
Example:

7. 3 Types of Differential Equations
Example:

8. 3 Types of Differential Equations
Example:

9. 3 Types of Differential Equations
Example:
This is the general solution

10. The constant can be written as part of the logarithm
Example:

11. Particular solution
Solve:
If when

12. Particular solution
Solve:
If when

13. Particular solution
Solve:
If when

14. Particular solution
Solve:

15. 2nd Types of Differential Equations
We can then integrate both sides.
This will obtain the general solution.

16. Example
A curve passes through the point (0, π/3) and its gradient at the point (x, y) is given by
Find the equation of the curve.
(Sidebotham)

17. General Solution
A curve passes through the point (0, π/3) and its gradient at the point (x, y) is given by
Find the equation of the curve.
(Sidebotham)

18. General Solution
A curve passes through the point (0, π/3) and its gradient at the point (x, y) is given by
Find the equation of the curve.
(Sidebotham)

19. Type 3

23. Testing solutions
Prove that is a solution to the differential equation

24. Do not try to integrate

25. Do not try to integrate
Substitute