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Assignment #7

Assignment #7 - Stephanie Campbell due at 11:55pm EST...

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Stephanie Campbell Assignment 7 MATH263, Fall 2010 due 12/01/2010 at 11:55pm EST. You may attempt any problem an unlimited number of times. 1. (1 pt) Find the indicated coefficients of the power series solution about x = 0 of the differential equation ( x 2 + 4 ) y - xy + y = 0 , y ( 0 ) = - 2 , y ( 0 ) = - 3 y = - 2 - 3 x + x 2 + x 4 + x 6 + x 8 + O ( x 9 ) 2. (1 pt) Find the indicated coefficients of the power series solution about x = 0 of the differential equation ( x 2 - x + 1 ) y - y + 6 y = 0 , y ( 0 ) = 0 , y ( 0 ) = 7 y = 7 x + x 2 + x 3 + x 4 + x 5 + O ( x 6 ) 3. (1 pt) Find the indicated coefficients of the power series solution about x = 0 of the differential equation y - ( sin x ) y = cos x , y ( 0 ) = 3 , y ( 0 ) = 8 y = 3 + 8 x + x 2 + x 3 + x 4 + O ( x 5 ) 4. (1 pt) Consider the differential equation 2 x ( x - 1 ) y + 3 ( x - 1 ) y - y = 0 which has a regular singular point at x = 0. The indicial equa- tion for x = 0 is r 2 + r + = 0 with roots (in increasing order) r 1 = and r 2 = Find the indicated terms of the following series solutions of the differential equation: (a) y = x r 1 ( 5 + x + x 2 + x 3 + x 4 + ... ) (b) y = x r 2 ( 4 + x + x 2 + x 3 + x 4 + ... ) The closed form of solution (a) is y = 5.
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