Question

Which of the following is false regarding quasilinear equations?

(a) All the terms with highest order derivatives of dependent variables occur linearly

(b) The coefficients of terms with highest order derivatives of dependent variables are functions of only lower order derivatives of the dependent variables

(c) Lower order derivatives can occur in any manner

(d) All the terms with lower order derivatives of dependent variables occur linearly

I got this question by my college director while I was bunking the class.

This interesting question is from Homogeneous Linear PDE with Constant Coefficient in division Partial Differential Equations of Engineering Mathematics

Answer 1

Correct answer is (d) All the terms with lower order derivatives of dependent variables occur linearly

The explanation is: A PDE is called as a quasi-linear if at the minimum one coefficient of the partial derivatives is a function of the dependent variable. For example, \(\frac{∂^2 u}{∂x^2}-u \frac{∂^2 u}{∂y^2}=0. \)