Question

The differential equation

${[1+{\left(\frac{dy}{dx}\right)}^2]}^3=C^2{\left[\frac{d^{2}y}{d{x}^2}\right]}^2$ is of

• A. $2^{nd}$ order and $3^{rd}$ degree
• B. $3^{rd}$ order and $2^{nd}$ degree
• C. $2^{nd}$ order and $2^{nd}$ degree
• D. $3^{rd}$ order and $3^{rd}$ degree

Answer 1

The correct option is C $2^{nd}$ order and $2^{nd}$ degree

Given
${[1+{\left(\frac{dy}{dx}\right)}^2]}^3=C^2{\left[\frac{d^{2}y}{d{x}^2}\right]}^2$

$\because$ It is free from fractions and radicals. So, order = 2 and degree = 2