Show that `x y=a e^x+b e^(-x)+x^2` is a solution of the differential equation `x(d^2y)/(dx^2)+2dy/dx-x y+x^2-2=0.`

Explanation

To show that \( xy = a e^x + b e^{-x} + x^2 \) is a solution of the differential equation

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

we will follow these steps:

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