Whenever we are asked to form a differential equation for a** family of curves**, we may not know, how many times we will have to differentiate it.

In order to avoid this confusion, we will have to see how many **arbitrary constants** the curve has.

If it has** 'n' constants**, then we will have to differentiate it **'n' times**, till the **arbitrary constants are eliminated**.

For Example:

Consider the equation of the curve

Y^{2}= 4ax

This equation has 1 arbitrary constant ‘a’.

So it is enough if we differentiate it once to eliminate the constant ‘a’ and form a differential equation.

Hence the Required Differential equation is **y ^{2}-2xyy’ =0 **

Here are couple of examples on clay6 based on the above tip: