Question

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

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

Answer 1

Answer: (C)

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