Question

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

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

Answer 1

Answer: (C)

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