If , then prove that…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If y=log⁡(x+x2+a2)y = \log(x + \sqrt{x^2 + a^2}) , then prove that (x2+a2)d2ydx2+xdydx=0(x^2 + a^2) \frac{d^2 y}{dx^2} + x \frac{dy}{dx} = 0 .

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