Question

If \(y=e^{m\sin^{-1}x}\) and \(y_n\) indicates \(n^{th}\) derivative of \(y\) with respect to \(x\), then which of the following relation is true?

• A. \((1+x^2)y_{n+2}-(2n+1)xy_{n+1}-(n^2+m^2)y_n=0\)
• B. \((1-x^2)y_{n+2}+(2n+1)xy_{n+1}-(n^2+m^2)y_n=0\)
• C. \((1-x^2)y_{n+2}+(2n+1)xy_{n+1}+(n^2+m^2)y_n=0\)
• D. \((1-x^2)y_{n+2}-(2n+1)xy_{n+1}-(n^2+m^2)y_n=0\)

Hint:

For successive derivative questions, first form the differential equation satisfied by \(y\), then apply Leibniz theorem to differentiate \(n\) times.

Answer 1

The Correct Option is D