Question

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

• A. $2$ and $2$
• B. $2$ and $1$
• C. $3$ and $2$
• D. $3$ and $3$
• E. $2$ and $4$

Answer 1

The correct option is C $3$ and $2$

Given, ${[2\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2]}^{3/2}=\frac{d^{3}y}{d{x}^3}$
On squaring both sides, we get
${[2\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2]}^3={\left(\frac{d^{3}y}{d{x}^3}\right)}^2$
Hence, order is $3$ and degree is $2$.