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 had been asked this question in unit test.

I need to ask this question from Formation of Ordinary Differential Equations by Elimination of Arbitrary Constants in division Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

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

Easy 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