How do we constitute the Differential Equations?

Question

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

Y²= 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 y²-2xyy’ =0 

 

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

https://clay6.com/qa/955

https://clay6.com/qa/953