DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS Henri Poincare ( - ) Let us consider the equation: = ... ( ) We see that equations ( ), ( ) and ( ) involve independent and/or dependent variable (variables) only but equation ( ) involves variables as well as derivative of the dependent variable y with respect to the independent variable x . Such an equation is called a differential equation . In general, an equation involving derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation.

A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation, e.g., d y +  = is an ordinary differential equation .... ( ) Of course, there are differential equations involving derivatives with respect to more than one independent variables, called partial differential equations but at this stage we shall confine ourselves to the study of ordinary differential equations only. Now onward, we will use the term ‘differential equation’ for ‘ordinary differential equation’.