Question

The order and degree of the differential equation $y^2=4a(x-a)$, where $a$ is an arbitrary constant, are respectively

• A. $1,2$
• B. $2,1$
• C. $2,2$
• D. $1,1$

Answer 1

The correct option is A $1,2$

Consider $y^2=4a(x-a)$

Differentiating on both sides we get

$2y\frac{dy}{dx}=4a$

$\Rightarrow y\frac{dy}{dx}=2a$

Differentiating again with respect to $x$ we get

$\Rightarrow y\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}\cdot \frac{dy}{dx}=0$

$\Rightarrow y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$

Thus the differential equation of$y^2=4a(x-a)$ is $y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$ whose order is $1$ and degree is $2$.