## Search This Blog

### Differential Equations

If you take the equation of a circle, x^2 + y^2 = 25, and differentiate it with respect to x, you get the following equation:
2x + 2y dy/dx = 0
or x + y dy/dx = 0      ... (i)
Equation (i) above is called a differential equation and it represents all those circles which have center at (0, 0) and any radius. All these circles form a family of circles.

Likewise, a differential equation represents a family of equations which correspond to some geometrical figure.

For example, the differential equation dy/dx = 4x + 6 represents a family of all parabolas because it is obtained by differentiating the equation of a parabola y = 2x^2 + 6x + 11, and the differential equation dy/dx = 1 represents a family of straight lines having slope 1.