Question

The degree of the differential equation $\frac{d^{2}y}{d{x}^2}=\frac{5y+\frac{dy}{dx}}{\sqrt{\frac{d^{2}y}{d{x}^2}}}$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. $5/2$

Answer 1

Answer: (B)

$\frac{d^{2}y}{d{x}^2}=\frac{5y+\frac{dy}{dx}}{\sqrt{d^{2}y/d{x}^2}}$
${\left(\frac{d^{2}y}{d{x}^2}\right)}^{3/2}=5y+\frac{dy}{dx}$
Squaring on both sides, ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3={\left(5y+\frac{dy}{dx}\right)}^2$
So, the degree of given differential equation is 3.