Question

Find the order and degree of the D.E \(\left (\frac{d^3 y}{dx^3}\right )-3\left (\frac{d^2 y}{dx^2}\right )+2\left (\frac{dy}{dx}\right )^4+y^3=0\).

(a) Order – 2, Degree – 4

(b) Order – 2, Degree – 1

(c) Order – 3, Degree – 1

(d) Order – 1, Degree – 3

The question was asked in an interview for job.

This intriguing question originated from Differential Equations Basics-2 in division Differential Equations of Mathematics – Class 12

Answer 1

The correct answer is (c) Order – 3, Degree – 1

The explanation is: In the differential equation, the highest order derivative is \(\frac{d^3 y}{dx^3}\). Therefore, the order of the differential equation is 3. The given is a polynomial equation in \(\frac{d^3 y}{dx^3}\). Hence, the degree will be the power raised to \(\frac{d^3 y}{dx^3}\) i.e. 1