notes5-5

# notes5-5 - EXAMPLE For the following diﬀerential equation...

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SECTION 5.5 SOLUTIONS NEAR REGULAR SINGULAR POINTS When x = 0 is a regular singular point for a diﬀerential equation P ( x ) y 00 + Q ( x ) y 0 + R ( x ) y = 0, we expect solutions to be a combination of Euler equation solutions and series solutions, that is, we expect to get a solution of the form y = x r X n =0 a n x n = X n =0 a n x n + r . We can always ﬁnd at least one solution of this form when x = 0 is a regular singular point. Various complications arise that make the second linearly independent solution sometimes diﬃcult to determine, and we won’t deal with these complications (See Section 5.6.).
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Unformatted text preview: EXAMPLE. For the following diﬀerential equation, determine the indicial equation, the recurrence relation, and the roots of the indicial equation. Find the series solution for x > corresponding to the larger root. If the roots are unequal and do not diﬀer by an integer, ﬁnd the series solution corresponding to the smaller root also. WE WILL BE SATISFIED WITH THE FIRST FOUR NONZERO TERMS OF THE SERIES. 2 x 2 y 00 + 3 xy + (2 x 2-1) y = 0 HOMEWORK: SECTION 5.5...
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## This note was uploaded on 02/14/2012 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas.

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