Question

The degree of the differential equation $\frac{d^{2}y}{d{x}^2}-\sqrt{\frac{dy}{dx}-3}=x$ ,equals

• A. 2
• B. 1/2
• C. 3
• D. 1

Answer 1

The correct option is A 2

Given, Differential equation is $\frac{d^{2}y}{d{x}^2}-\sqrt{(}\frac{dy}{dx}-3)=x$

$\Rightarrow \frac{d^{2}y}{d{x}^2}-x=\sqrt{(}\frac{dy}{dx}-3)$

On squaring both sides,

$\Rightarrow (\frac{d^{2}y}{d{x}^2}-x{)}^2=(\sqrt{(}\frac{dy}{dx}-3){)}^2$

$\Rightarrow (\frac{d^{2}y}{d{x}^2}{)}^2+x^2-2x\frac{dy}{dx}=(\frac{dy}{dx}-3)$

The degree of the equation is the power of the highest order Differential term in the equation. Here it is $2$(since power of $\frac{d^{2}y}{d{x}^2}$ in the equation is $2$)

Hence the degree of the equation is $2$