Question

Which of the following is an example of non-linear differential equation?

(a) y=mx+c

(b) x+x’=0

(c) x+x^2=0

(d) x”+2x=0

I had been asked this question during an interview.

My question is from First Order Non-Linear PDE topic in portion Partial Differential Equations of Engineering Mathematics

Answer 1

The correct answer is (c) x+x^2=0

The best I can explain: For a differential equation to be linear the dependent variable should be of first degree. Since in equation x+x^2=0, x^2 is not a first power, it is not an example of linear differential equation.