|
Order of a Differential EquationThe order of a differential equation is the order of the highest derivative included in the equation.Example 1: State the order of the following differential equations 
Solution to Example 1 1. The highest derivative is dy/dx, the first derivative of y. The order is therefore 1. 2. The highest derivative is d2y / dx2, a second derivative. The order is therefore 2. 3. The highest derivative is the second derivative y". The order is 2. 4. The highest derivative is the third derivative d3 / dy3. The order is 3.
Linearity a Differential EquationA differential equation is linear if the dependent variable and all its derivative occur linearly in the equation.Example 2: Which of these differential equations are linear? 
Solution to Example 2 1. Both dy/dx and y are linear. The differential equation is linear. 2. The term y3 is not linear. The differential equation is not linear. 3. The term ln y is not linear. This differential equation is not linear. 4. The terms d3y / dx 3, d2y / dx 2 and dy / dx are all linear. The differential equation is linear.
Example 3:
Example 4:
Exercises: Determine the order and state the linearity of each differential below.
Answers to Above Exercises 1. order 3 , non linear. 2. order 1 , linear. 3. order 1 , non linear. 4. order 2 , linear.
More references on
Differential Equations
|