CUET · MATHS · PYQ PAPER 2025
If \(y=e^{a \cos ^{-1} x},-1< x< 1\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}\) is equal to
- A \(a^2 y\)
- B \(-a^2 y\)
- C ay
- D \(-a y\)
Answer & Solution
Correct Answer
(A) \(a^2 y\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} = e^{a \cos ^{-1} x} \cdot a \cdot \frac{-1}{\sqrt{1-x^2}} = \frac{-a y}{\sqrt{1-x^2}}\) \(\sqrt{1-x^2} \frac{d y}{d x} = -a y\) \(\frac{d}{d x} \left( \sqrt{1-x^2} \frac{d y}{d x} \right) = \frac{d}{d x} (-a y)\)…
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