JEE Main & Advanced Mathematics Differential Equations Formation of Differential Equation

Formulating a differential equation from a given equation representing a family of curves means finding a differential equation whose solution is the given equation. The equation so obtained is the differential equation of order  for the family of given curves.

Algorithm for formation of differential equations

Step (i) : Write the given equation involving independent variable  (say), dependent variable  (say) and the arbitrary constants.

Step (ii) : Obtain the number of arbitrary constants in step (i). Let there be  arbitrary constants.

Step (iii) : Differentiate the relation in step (i)  times with respect to .

Step (iv) : Eliminate arbitrary constants with the help of n equations involving differential coefficients obtained in step (iii) and an equation in step (i). The equation so obtained is the desired differential equation.