DIFFERENTIAL EQUATIONS Differential equation An equation contains dependent

DIFFERENTIAL EQUATIONS

Differential equation An equation contains dependent variable, independent variable and the derivatives of dependent variable with respect to independent variable is called a differential equation. Examples:

Order of the differential equation The order of differential equation is defined as the highest order derivative which occur in the equation. Examples: is a differential equation of order 1 is a differential equation of order 2

Degree of the differential equation The degree of differential equation is defined as the integral power of highest derivative occur in the differential equation. . Examples: is a differential equation of degree 1 is a differential equation of order 2

Linear and non-linear differential equation A differential equation is said to be linear if dependent variable and its derivatives occur only in first degree and are not multiplied together, otherwise it is called nonlinear. Examples: . is a linear differential equation. is a non-linear differential equation. is a linear differential equation.

Solution of 1 st order and 1 st degree ordinary differential equation by variable separable method Separation of the variable is done when the differential equation can be written in the form of dy/dx= f(x)g(y), where f is the function of x only and g is the function of y only. We may rewrite this problem as dy/g(y)= f(x)dx. Now integrating both sides and we will have solution of the differential equation.