Word Count : 444

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We are given the function \( y = e^m \sin^{-1}x \) and need to show that: \[ (1 - x^2) y_2 - x y_1 - m^2 y = 0 \] We also need to find the value of: \[ (1 - x^2) y_{n+2} - (2n + 1) x y_{n+1} \] ### Step 1: Derivatives of \( y = e^m \sin^{-1}x \) We start by finding the derivatives of \( y \). 1. First, differentiate _______ _____ _____ ______ _________.
___ _________ ______ _______ _________ _______ ________ ____ _______ ______ ____.
________ ____ _____ _________ ___ _______.
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_____ _________ ________ ____ _____.
______ ____ ________ _______ __________.
_________ ___ _______ ___ _______.
________ _____ _____ _______ ___ _______ _____.
_____ __________ _____ __________ ______ _____ _____ __________ _____ ____ _____ ________.
____ ____ _______ __________ _____ ____.
_____ __________ ________ ___ ___ ______ _____ _______.
__________ ________ ___ _________ ___ ________ ______ __________ ___ __________ _________ __________.
_____ _____ ________ ___ ___ __________.
__________ ___ __________ _________ __________ ___ _____ _____ ______ __________ __________ ______.
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________ _____ ___ ________ ______ _______ ___ _________ ________ _______.
_______ __________ ________ __________ _____ _________.
_____ _________ ____ _________ ________ ___ __________ _________.
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_______ _______ ________ ____ ______ _________ _____ ____ _______.
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______ ___ ______ _______ __________.
_______ _________ ______ ___ _________ _______ ______ ____ _________ _______.
________ _____ ___ _______ _______ ___.
________ ______ ________ _______ ______ ______ ____ ______.
____ __________ _______ _________ _______ ___ ____ ____ ______ ___ ______.
________ ___ _____ ___ _______.
_______ _____ ___ _____ _______ ___ ___.
_________ _________ ______ __________ ________ __________ __________.
________ _____ ____ _____ _________ ______ _________ ______ ________ _____ ________.
________ _______ ____ _______ _______.
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