Question

The degree and order of the differential equation ${\left[1+{\left(\frac{dy}{dx}\right)}^3\right]}^{7/3}=7\left(\frac{d^{2}y}{d{x}^2}\right)$ respectively are

• A. $3$ and $7$
• B. $3$ and $2$
• C. $7$ and $3$
• D. $2$ and $3$

Answer 1

Answer: (B)

Given, differential equation is
${\left[1+\left(\frac{dy}{dx}\right)\right]}^{\frac{7}{3}}=7\left(\frac{d^{2}y}{d{x}^2}\right)$
On cubing both sides, we get
${\left[1+{\left(\frac{dy}{dx}\right)}^3\right]}^7=7^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^3$
Here, we see that highest order derivative is $2$, whose degree is $3$.
Hence, degree $=3$ end order $=2$