Differential Equation

Earlier, we have studied about derivative f’(x) of function f (x) with respect to an independent variable, at each x in its domain of definition. Further we have studied about function f(x) and its derivative g(x), i.e., finding f (x) whose derivative is the function g(x), such that f’(x)=g(x), where y=f(x). Such equation is known as Differential Equation. So, A Differential Equation is an equation with a function and one or more of its derivatives.

Order of Differential Equation

The highest order derivative of the dependent variable with respect to the independent variable in the given differential equation is defined as Order of a Differential Equation.

Degree of a Differential Equation

The degree of a polynomial Differential Equation is the highest power (positive integral index) of the higher order derivative.

Differential Equation Solution

A solution of a differential equation is an expression for the dependent variable in terms of the independent variables which satisfies the relation.

• General Solution of Differential Equation : The solution which containing arbitrary constants is called the general solution of the differential equation.
• Particular Solution of Differential Equation : The solution free from arbitrary constant (obtained from general solution for [particular value of arbitrary constants is called Particular Solution)

Differential Equation Solution – Example

Differential Equation solution Verification