If you take the equation of a circle, x2+y2=25, and differentiate it with respect to x, you get the following equation:
Likewise, a differential equation represents a family of equations which correspond to some geometrical figure.
For example, the differential equation dydx=4x+6 represents a family of all parabolas because it is obtained by differentiating the equation of a parabola y=2x2+6x+11, and the differential equation dydx=1 represents a family of straight lines having slope 1.
2x+2ydydx=0
or x+ydydx=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 dydx=4x+6 represents a family of all parabolas because it is obtained by differentiating the equation of a parabola y=2x2+6x+11, and the differential equation dydx=1 represents a family of straight lines having slope 1.
