Question

Which of these equations are used to classify PDEs?

(a) \(b(\frac{dy}{dx})-c=0\)

(b) \(a(\frac{dy}{dx})^2-b(\frac{dy}{dx})=0\)

(c) \((\frac{dy}{dx})^2-(\frac{dy}{dx})+1=0\)

(d) \(a(\frac{dy}{dx})^2-b(\frac{dy}{dx})+c=0\)

I got this question during a job interview.

My question is from Classification of PDE topic in division Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics

Answer 1

Correct answer is (d) \(a(\frac{dy}{dx})^2-b(\frac{dy}{dx})+c=0\)

For explanation: \(a(\frac{dy}{dx})^2-b(\frac{dy}{dx})+c=0\) is the characteristic equation for searching simple wave solutions. This is used to find the type of PDEs by substituting a, b and c by the coefficients of the second order derivatives of the given PDE.