Show that `A x^2+B y^2=1` is a solution of the differential equation `x{y\ (d^2y)/(dx^2)+((dy)/(dx))^2}=y(dy)/(dx)dot`

Explanation

To show that the equation \( Ax^2 + By^2 = 1 \) is a solution of the differential equation

\[ x y \frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 = y \frac{dy}{dx}, \]

we will follow these steps:

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