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Solve this following

Question:

If $y=e^{a \cos -1 x},-1 \leq x \leq 1$, show that $\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-a^{2} y=0$

Solution:

$\Rightarrow\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-a^{2} y-x \frac{d y}{d x}=0$

Hence Proved

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