If , then prove that…

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

Problem

y = (x + \sqrt{x^2 + 1})^m

, then prove that

(x^2 + 1)y'' + xy' - m^2 y = 0

Related theory

Higher-Order Derivatives
Advanced Differentiation
Logarithmic Differentiation
Differentiation Rules
Logarithmic differentiation and differentiation of one function w.r.t. another
Continuity and Differentiability

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