Show that `y=A x+B/x ,x!=0` is a solution of the differential equation `x^2(d^2y)/(dx^2)+x(dy)/(dx)-y=0`

Explanation

To show that \( y = Ax + \frac{B}{x} \) is a solution of the differential equation

\[ x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, \]

we will follow these steps:

...