CUET Preparation Today
The differential equation of the family of parabolas having vertex at the origin and the y-axis as the axis of symmetry, is |
$2y_1=-y=0$ $y_1+xy=0$ $xy_1-2y=0$ $yy_1-2x=0$ |
$xy_1-2y=0$ |
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. |
