Question

Which of the following is one of the criterions for linearity of an equation?

(a) The dependent variable and its derivatives should be of second order

(b) The dependent variable and its derivatives should not be of same order

(c) Each coefficient does not depend on the independent variable

(d) Each coefficient depends only on the independent variable

I had been asked this question in quiz.

This question is from First Order Linear PDE in portion Partial Differential Equations of Engineering Mathematics

Answer 1

Correct choice is (d) Each coefficient depends only on the independent variable

Easiest explanation: The two criterions for linearity of an equation are:

The dependent variable y and its derivatives are of first degree.

 Each coefficient depends only on the independent variable