Hypergeometric Function D.E. Solution | Near x = -1 | No Quotation Marks

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SUMMARY

The discussion focuses on solving the differential equation (1-x²)y'' - (5x² - 9)/5x y' + 8y = 0 near x = -1 using Hypergeometric functions. The main challenge identified is the problematic coefficient of y', specifically 9/5x. The user successfully derived the general solution, confirming the application of Hypergeometric functions in this context.

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  • Understanding of differential equations and their solutions
  • Familiarity with Hypergeometric functions
  • Knowledge of series expansions near singular points
  • Basic calculus, particularly derivatives and their applications
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  • Learn about singular points in differential equations
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zorro
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Homework Statement

Find the general solution in terms of Hypergeometric functions near x = -1 :
(1-x2)y'' - (5x2 - 9)/5x y' + 8y = 0

The Attempt at a Solution



Here the coefficient of y' contains 9/5x which causes problem. The general form contains the coefficient of y' as A+Bx

How do I solve this?
 
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Solved it.
 

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