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

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

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

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

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

3 Types of Differential Equations Example:

3 Types of Differential Equations Example:

3 Types of Differential Equations Example:

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

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

Particular solution Solve: If when

Particular solution Solve: If when

Particular solution Solve: If when

Particular solution Solve:

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

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)

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)

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)

Type 3

Testing solutions Prove that is a solution to the differential equation

Do not try to integrate

Do not try to integrate Substitute