The differential equation of the family of parabolas having vertex at the origin and the y-axis as the axis of symmetry, is
Answer & explanation
Correct answer: option 3
The correct answer is option (3) : $xy_1-2y=0$
The equation of the family of parabolas having vertex at the origin and the y-axis as the axis of symmetry is
$y = ax^2$
$⇒\frac{dy}{dx}= 2ax$
$⇒\frac{dy}{dx}= \frac{2y}{x}$ $[∵y=ax^2 ⇒a=\frac{y}{x^2}]$
$⇒xy_1-2y=0$
This is the required differential equation.