Revision: Ordinary Differential Equations Mathematics HSC Science Class 12 Tamil Nadu Board of Secondary Education

An equation involving independent variable(s), dependent variable(s), derivatives of the dependent variable (s) with respect to the independent variable(s), and a constant is called a differential equation.

The order of the highest differential coefficient (or the highest order derivative appearing in a differential equation) is the order of the differential equation.

The highest exponent of the highest derivative is called the degree of a differential equation, provided exponents of each derivative and an unknown variable appearing in the differential equation are non-negative integers.

1. Basic Idea:

• Form a differential equation from a given equation by eliminating arbitrary constants

2. Steps:

• Identify arbitrary constants in the given equation

• Differentiate the equation with respect to x as many times as the number of constants

• Eliminate constants from the obtained equations

3. Important Rule:

• Number of differentiations = number of arbitrary constants

4. Final Result:

• After eliminating constants → required differential equation is obtained

6. Important Note:

• A differential equation represents a family of curves