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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.