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

Explanation

To show that \( y = a \cos(\log x) + b \sin(\log x) \) is a solution of the differential equation

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

we will follow these steps:

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