Equation of the family of an ellipse having foci on the y-axis and centers at the origin can be represented by
\(\cfrac{x^2}{a^2}-\cfrac{y^2}{b^2}=1\)(1)
Differentiating the above equation with respect to x on both sides, we have,
Again differentiating the above equation with respect to x on both sides, we have,
Rearranging the above equation
\(xy\cfrac{d^2y}{dx^2}+x\left(\cfrac{dy}{dx}\right)^2-y\cfrac{dy}{dx}=0\)
This is the required differential equation.
