M427K-F10-HW7 - x . That is, nd the recurrence relation for...

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M427K , 55330, Oct 11, 2010 Homework 7 , due Oct 18 5.1.5 Determine the radius of convergence of the given power series. s n =1 (2 x + 1) n n 2 . 5.1.7 Determine the radius of convergence of the given power series. s n =1 ( - 1) n n 2 ( x + 2) n 3 n . 5.1.13 Determine the Taylor series about the point x 0 for the given function f . Also deter- mine the radius of convergence of the series. f ( x ) = ln( x ) , x 0 = 1 . 5.2.16 Find the power series solution of the given initial value problem about the point x 0 = 0. That is, ±nd the recurrence relation for the coe²cients of the series, and determine the ±rst ±ve nonzero terms. ( 2 + x 2 ) y ′′ - xy + 4 y = 0 , y (0) = - 1 , y (0) = 3 . 5.2.14 Find the power series solution of the given di³erential equation about the given point
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Unformatted text preview: x . That is, nd the recurrence relation for the coecients of the series, and determine the rst four terms for the series solutions y 1 and y 2 (see the remark below). 2 y + ( x + 1) y + 3 y = 0 , x = 2 . 5.3.6 Determine a lower bound for the radius of convergence of series solutions about each given point x for the given dierential equation. ( x 2-2 x-3 ) y + xy + 4 y = 0; x = 4 , x =-4 , x = 0 . Remark. y 1 and y 2 denote the solutions that satises y 1 ( x ) = 1, y 1 ( x ) = 0, and y 2 ( x ) = 0, y 2 ( x ) = 1, respectively....
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