TS EAMCET · Maths · Differentiation
\(y=e^{a \sin ^{-1} x} \Rightarrow\left(1-x^2\right) y_{n+2}-(2 n+1) x y_{n+1}\) is equal to
- A \(-\left(n^2+a^2\right) y_n\)
- B \(\left(n^2-a^2\right) y_n\)
- C \(\left(n^2+a^2\right) y_n\)
- D \(-\left(n^2-a^2\right) y_n\)
Answer & Solution
Correct Answer
(C) \(\left(n^2+a^2\right) y_n\)
Step-by-step Solution
Detailed explanation
Given, \(\quad y=e^{a \sin ^{-1} x}\) On differentiating w.r.t. \(x\), we get \(\begin{aligned} & y_1=e^{a \sin ^{-1} x} a \cdot \frac{1}{\sqrt{1-x^2}} \\ \Rightarrow \quad & y_1 \sqrt{1-x^2}=a y \\ \Rightarrow \quad & \left(1-x^2\right) y_1^2=a^2 y^2 \end{aligned}\) Again,…
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