Question

What is the nature of the equation, \(xy^3 (\frac{dy}{dx})^2+yx^2+\frac{dy}{dx}=0\)?

(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

The question was asked during an interview.

I'd like to ask this question from Formation of Ordinary Differential Equations by Elimination of Arbitrary Constants in portion Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

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

For explanation I would say: 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.