Question

The order and degree of the differential equation ${[4+{\left(\frac{dy}{dx}\right)}^2]}^{2/3}=\frac{d^{2}y}{d{x}^2}$ are

• A. 2,2
• B. 3,3
• C. 2,3
• D. 3,2

Answer 1

The correct option is C

2,3

Here power on the differential coefficient is fractional, therefore change it into positive integer, so
${[4+{\left(\frac{dy}{dx}\right)}^2]}^{2/3}=\frac{d^{2}y}{d{x}^2}\Rightarrow {[4+{\left(\frac{dy}{dx}\right)}^2]}^2={\left[\frac{d^{2}y}{d{x}^2}\right]}^3$
Hence order is 2 and degree is 3.