The differential equation representing the family of curves $y^2=2 c(x+\sqrt{c})$, where c is a positive parameter, is of
Answer & explanation
Correct answer: option 1
We have,
$y^2=2 c(x+\sqrt{c})$ .......(i)
$\Rightarrow 2 y y_1=2 c$
$\Rightarrow y y_1=c$ .......(ii)
Eliminating c from (i) and (ii), we get
$y^2=2 y y_1\left(x+\sqrt{y y_1}\right)$
$\Rightarrow y-2 x y_1=\left(\sqrt{y} y_1\right)^{3 / 2} \Rightarrow\left(y-2 x y_1\right)^2=\left(y y_1\right)^3$
Clearly, it is a differential equation of order one and degree 3.