Given the differential equation: (1-x)y"+y=0, x0=0 Find: Seek the power series solution for the differential equation about the given point x0; find the recurrence relation Find the first four terms in each of the two solutions, y1 and y2 (unless the series terminates sooner) By evaluating the Wronskian, W(y1,y2)(x0), show that y1 and y2 form a fundamental set of solutions If possible, find the general term in each solution

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Given the differential equation:

(1-x)y"+y=0, x0=0

Find:

  • Seek the power series solution for the differential equation about the given point x0; find the recurrence relation
  • Find the first four terms in each of the two solutions, y1 and y2 (unless the series terminates sooner)
  • By evaluating the Wronskian, W(y1,y2)(x0), show that y1 and y2 form a fundamental set of solutions
  • If possible, find the general term in each solution
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