## Sunday, May 25, 2008

### Differential Equations - Revision Points 1

JEE syllabus

- Formation of ordinary differential equations
- Solution of homogeneous differential equations
- Variables separable method,
- Linear first order differential equations.

Differential equation is an equation involving derivatives of a dependent variable with respect to one or more independent variables.

Example: d²y/dx²+ y = x²

Order and degree are two attributes of a differential equation.

The order of a differential equation is the order of the highest differential coefficient involved. If second order derivative is present in the differential equation, the order of the equation is two or it is of second order. The equation give above as an example is a second order equation as d²y/dx² a second order derivative of y is present in the equation.

In the equation, the power to which the higher differential coefficient or derivative is raised is known as the degree of the equation.

Formation of ordinary differential equations

If we are given a relation between variables x and y containing a number of arbitrary constants, we cn form a differntial equation from it by differntiating the given relation enough times so as to eliminate all the arbitrary constants.