Verify that `y=log(x+sqrt(x^2+a^2))^2` satisfies the differential equation `(a^2+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=0.`

Explanation

To verify that \( y = \log(x + \sqrt{x^2 + a^2})^2 \) satisfies the differential equation

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

we will follow these steps:

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