Question

The degree of the differential equation
$\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/3} =\frac{d^{2}y}{dx^{2}} $ is

• A. $1$
• B. $5$
• C. $\frac{10}{3}$
• D. $3$

Answer 1

Answer: (D)

The given differential equation is

$\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/3} =\frac{d^{2}y}{dx^{2}} $

$\Rightarrow \left(\frac{d^{2}y}{dx}\right)^{3} = \left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5}$

From above it is clear that the degree of the given differential equation is $3$.