Question

The differential equation of family of coaxial circle $x^2+y^2+2\lambda x+c=0$ is

• A. $y.\frac{d^{2}y}{{dx}^2}+{\left(\frac{dy}{dx}\right)}^2+1=0$
• B. $y.\frac{d^{2}y}{{dx}^2}+{\left(\frac{dy}{dx}\right)}^2=0$
• C. $\left(\frac{d^{2}y}{{dx}^2}\right)+{\left(\frac{dy}{dx}\right)}^2+1=0$
• D. $\frac{d^{2}y}{{dx}^2}+{\left(\frac{dy}{dx}\right)}^2=0$

Answer 1

The correct option is A $y.\frac{d^{2}y}{{dx}^2}+{\left(\frac{dy}{dx}\right)}^2+1=0$

$x^2+y^2+2\sqrt{x}+c=0$

$\Rightarrow 2x+2y\frac{dy}{dx}+2\sqrt{\varphi }=0$

$\Rightarrow x+y\frac{dy}{dx}+\sqrt{\varphi }=0$

$\Rightarrow 1+{\left(\frac{dy}{dx}\right)}^2+y\frac{d^{2}y}{d{x}^2}=0$

$\Rightarrow y\left(\frac{d^{2}y}{dx}\right)+{\left(\frac{dy}{dx}\right)}^2+1=0$