Given that $y={{\sin }^{-1}}x$, prove that \(\left( 1-{{x}^{2}} \right)\frac{{{\mathrm{d

Question

Given that $y={{\sin }^{-1}}x$, prove that $\left( 1-{{x}^{2}} \right)\frac{{{\mathrm{d}}^{3}}y}{\mathrm{d}{{x}^{3}}}-3x\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}-\frac{\mathrm{d}y}{\mathrm{d}x}=0$.

Accepted Answer

$(1-x^2)y^{\prime\prime\prime}-3xy^{\prime\prime}-y^{\prime}=0$ for $-1<x<1$, as shown.

Techniques of Differentiation - Derivatives of Inverse Trigonometric Functions

Techniques of Differentiation - Derivatives of Inverse Trigonometric Functions

Solution:

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