Question

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

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

Answer 1

The correct option is A $2,3$

The given differential equation is
${[1+{\left(\frac{dy}{dx}\right)}^3]}^{\frac{7}{3}}=7\frac{d^{2}y}{d{x}^2}$
$\Rightarrow {[1+{\left(\frac{dy}{dx}\right)}^3]}^7={\left(7\frac{d^{2}y}{d{x}^2}\right)}^3$ ....[cubing both sides]
$\Rightarrow {[1+{\left(\frac{dy}{dx}\right)}^3]}^7=343{\left(\frac{d^{2}y}{d{x}^2}\right)}^3$
i.e., Order: the highest derivative of $\frac{d^{2}y}{d{x}^2}$ is $2$.
Degree of the highest order derivative is $3$.
Hence, the correct answer from the given alternatives is option $A$.