Question

The order and degree of the differential equation ${\left(1+{\left(\frac{dy}{dx}\right)}^2\right)}^{\frac{3}{4}}={\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}$ is

• A. (2, 4)
• B. (2, 3)
• C. (6, 4)
• D. (6, 9)
• E. (2, 12)

Answer 1

Answer: (A)

Given differential equation can be rewritten as ${\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^{\frac{3}{4}\times 12}={\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}\times 12}$
$\Rightarrow$ ${\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^9={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$
Here, we see that order of highest derivative is 2 and degree is 4.