Question

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

• A. $2$
• B. $1$
• C. $3$
• D. $ \frac{2}{3}$

Answer 1

Answer: (C)

Given differential equation is .
$\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{2/ 3} = \frac{d^{3}y}{dx^{3}} $
Cubing both sides, we get
$\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{2} = \left( \frac{d^{3}y}{dx^{3}}\right)^3 $
$ \therefore $ Order = 3.