Question

Which one of the following is not a criterion for linearity of an ordinary differential equation?

(a) The dependent variable y and its derivatives are of first degree

(b) The derivatives of the dependent variable y should be of second degree

(c) No product terms of y and/or any of its derivatives are present

(d) No transcendental functions of y and/or its derivatives occur

This question was posed to me during a job interview.

My question is based upon Basic Definitions in division Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

Right answer is (b) The derivatives of the dependent variable y should be of second degree

To explain: The criterions for linearity of an ordinary differential equation are:

The dependent variable y and its derivatives are of first degree

 No product terms of y and/or any of its derivatives are present

 No transcendental functions of y and/or its derivatives occur