Question

Which of the following is true with respect to formation of differential equation by elimination of arbitrary constants?

(a) The given equation should be differentiated with respect to independent variable

(b) Elimination of the arbitrary constant by replacing it using derivative

(c) If ‘n’ arbitrary constant is present, the given equation should be differentiated ‘n’ number of times

(d) To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable

I have been asked this question in class test.

This intriguing question comes from Method of Separation of Variables topic in portion Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

The correct choice is (d) To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable

Easiest explanation: Consider a general equation, f(x,y,c)=0 ……………………………………… (1)

To form a differential equation by elimination of arbitrary constant, the following steps need to be followed:

Differentiate (1) with respect to x

 In case of ‘n’ arbitrary constants, the equation should be differentiated ‘n’ number of times

 Eliminate the arbitrary constant using (1) and the derivatives