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.
Consider the equation of the curve
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 y2-2xyy’ =0
Here are couple of examples on clay6 based on the above tip: