Question

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

• A. $3,2$
• B. $3,10$
• C. $2,3$
• D. $3,5$

Answer 1

Answer: (A)

Given differential equation is

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

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

From above it is clear that the order and degree of the given differential equation are $3$ and $2$ respectively.