Question

The differential equation of the family of curves $y^2=4a(x+a)$, where a is an arbitrary constant, is

• A. $y[1+{\left(\frac{dy}{dx}\right)}^2]=2x\frac{dy}{dx}$
  
• B. $y[1-{\left(\frac{dy}{dx}\right)}^2]=2x\frac{dy}{dx}$
  
• C. $\frac{d^{2}y}{d{x}^2}+2\frac{dy}{dx}=0$
• D. ${\left(\frac{dy}{dx}\right)}^3+3\frac{dy}{dx}+y=0$

Answer 1

The correct option is B

$y[1-{\left(\frac{dy}{dx}\right)}^2]=2x\frac{dy}{dx}$

Given $y^2=4a(x+a).$ Differentiating, $2y\left(\frac{dy}{dx}\right)=4a$
Eliminating a from (i) and (ii), required equation is
$y[1-{\left(\frac{dy}{dx}\right)}^2]=2x\frac{dy}{dx}$