Word Count : 389

---

The given differential equation is: \[ 4x y'' + 2y' + y = 0 \] We will use the Frobenius method, which assumes a solution in the form of a power series: \[ y(x) = \sum_{n=0}^{\infty} a_n x^{n+r} \] ### Step 1: Compute Derivatives First, differentiate \( y(x) \): \[ y'(x) = \sum_{n=0}^{\infty} a_n (n+r) x^{n+r-1} \] \[ y''(x) = \sum_{n=0}^{\infty} a_n (n+r)(n+r-1) x^{n+r-2} _________ ______ _____ ___ _________ ____ _________ __________ ____.
_____ ______ _______ ______ _________ ______ ___ ___ ________.
_____ ______ ______ ____ _________ _______.
__________ __________ __________ ____ ____ _____ _______ ________ ________ _____.
__________ ___ _____ ______ _____ _______.
________ ___ _________ __________ _____ ____ ________ _____ ___.
__________ _____ ____ _______ ___ _________ ______ _______ _______ ____.
__________ ___ _____ ________ _____ _______ _________ ______ _____ ________ _______.
__________ ______ ________ _____ ____ ___ _________ ______ ___ __________.
___ ________ ______ ________ _________ _____ _____ _____ ______ ______ _________ ____.
__________ ______ ________ _______ ________ _______ _____ _______.
________ ______ _________ _______ ______ _____ __________.
_________ _________ _____ ______ ___ _______ ___ __________.
_________ _____ __________ ______ ________.
_________ __________ _______ ________ _________ _____.
_____ __________ ______ ________ _______ ___ __________ ____ ____ _________ _________ _______.
__________ __________ ______ _____ ________.
_____ ____ _______ _________ __________ _____ ____.
______ ___ _____ ______ ______ _______.
__________ _________ ___ _________ ________ ____ _______ __________ ____ __________.
____ _________ _____ ______ ________ _________ _____ __________ ________ __________.
__________ _____ _________ ___ __________ ______ __________ _____ __________ _______.
___ ___ _______ ___ ______.
______ _________ ________ __________ ___ ________.
___ _________ _______ _______ _______ ____ ____ _______ ______ _______.
_________ ______ _______ _______ ______ _________ ____ _______.
_____ ___ _____ ________ ______ ____ ____.
_______ ____ __________ _____ ___ ____ ___.
______ _____ _________ ________ _______ ______ _____.
________ ______ ______ ______ __________ ____ _________ ____ ________.
_____ _____ _________ ___ _______ _____ _________ ______ _____ _____ ______.
_____ ____ _____ _____ ________ __________ _________ _________.
____ _____ ____ ___ ____.
_________ ________ _____ ____ _________.
_____ _______ _______ ______ ______.
______ ________ _______ ___ ___ _________ ____ _________ _______ ___.
___ _____ _____ _________ ________ ____ __________ __________.
__________ ____ _______ __________ ________ _______.
___ ___ _____ _____ __________ _____ __________ _________.
___ __________ _______ _____ _______ ____ ____ ________ ______.
_________ ______ ________ _______ ________.
Get Full Answer on WhatsApp