Question

Degree of the differential equation $\frac{d^{2}y}{d{x}^2}=\sqrt[3]{31+(\frac{dy}{dx}{)}^4}$ is .

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Degree of a differential equation is defined as the highest power of highest derivative in it after differential equation is cleared of radicals and fractions so far as the derivatives are concerned. $\frac{dy}{dx}$ is inside the radical symbol(cube root).
Cubing both the sides, $(\frac{d^{2}y}{d{x}^2}{)}^3=1+(\frac{dy}{dx}{)}^4$
The degree will be power of $\frac{d^{2}y}{d{x}^2}$ which is 3.