Question

The degree and the order of the differential equation $\frac{d^{2}y}{d{x}^2}=\sqrt[3]{31+{\left(\frac{dy}{dx}\right)}^2}$ respectively are

• A. 2 and 3
• B. 3 and 2
• C. 2 and 2
• D. 3 and 3

Answer 1

The correct option is B 3 and 2

$\frac{d^{2}y}{d{x}^2}=\sqrt[3]{31+{\left(\frac{dy}{dx}\right)}^2}$
$\Rightarrow {\left(\frac{d^{2}y}{d{x}^2}\right)}^3=1+{\left(\frac{dy}{dx}\right)}^2$
Highest order derivative involved is of 2nd order and its power is 3.
Therefore, order is 2 and degree is 3.