## 10

## Ordinary Differential Equations

An ordinary differential equation is an equation containing one independent variable and one dependent variable and at least one of its derivatives with respect to the independent variable. We know that a differential equation of *n*th order has *n* independent arbitrary constants in its general solution. Therefore, we need *n* conditions to compute the numerical solution of an *n*th order differential equation.

##### 10.1 INITIAL VALUE PROBLEMS AND BOUNDARY VALUE PROBLEMS

Problems in which all the initial conditions are specified at the initial point only are called initial value problems or marching problems. Thus, in an initial value problem, all the auxiliary conditions are specified at a point, for example, value of ...