The differential equation satisfied by the system of parabolas \({y}^{2}=4a(x+a)\) is : [JEE Main 2021, 18 Mar (Shift 1)…

\(y{\left(\frac{dy}{dx}\right)}^{2}-2x\left(\frac{dy}{dx}\right)-y=0\)

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

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

\(y\left(\frac{dy}{dx}\right)+2x\left(\frac{dy}{dx}\right)-y=0\)