If \( y=\log \left[x+\sqrt{x^{2}+a^{2}}\right] \), then prove that \( \left(x^{2}+a^{2}\right) \...

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If \( y=\log \left[x+\sqrt{x^{2}+a^{2}}\right] \), then prove that \( \left(x^{2}+a^{2}\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=0 \)
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