Question

\(xy^3(\frac{dy}{dx})^2+yx^2+\frac{dy}{dx}=0\) is a _____________

(a) Second order, third degree, linear differential equation

(b) First order, third degree, non-linear differential equation

(c) First order, third degree, linear differential equation

(d) Second order, third degree, non-linear differential equation

This question was addressed to me during a job interview.

The query is from First Order Nonlinear Differential Equations topic in portion Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

The correct choice is (b) First order, third degree, non-linear differential equation

Easy explanation: Since the equation has only first derivative, i.e. \((\frac{dy}{dx}),\) it is a first order equation.

Degree is defined as the highest power of the highest order derivative involved. Hence it is 2.

The equation has one/more terms having a variable of degree two/higher; hence it is non-linear.