Question

From the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of $X-$axis.

Answer 1

$y^2=4ax$

Now, $y^2=4ax$

$\Rightarrow 2y\left(\frac{dy}{dx}\right)=4a$

$\Rightarrow 2y{y}_1=\left(\frac{y^2}{x}\right)$

$\Rightarrow 2x{y}_1=y$

$\Rightarrow 2x{y}_1-y=0$.