7_HW - = 0, x o = 0 (d) y + xy + 2 y = 0, x o = 0 (e) (1 +...

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Math 2233 Homework Set 7 1. Find the general solution to the following differential equations. If initial conditions are specified, also determine the solution satisfying those initial conditions. (a) y (4) +2 y + y =0 (b) y - y - y + y =0 (c) y - 3 y +3 y - y = 0, y (0) = 1, y (0) = 2, y (0) = 3 (d) y +5 y - y - 5 y =0 (e) y (4) - 9 y =0 2. Combine each of the following power series expressions into a single power series. (a) n =0 ( n + 1)( x - 1) n - 1 + n =0 n ( x - 1) n (b) n =0 ( n +1) a n +2 x n +1 + n =0 na n x n - 1 (c) ( x - 1) n =0 na n x n - 1 + n =0 a n x n (d) x n =0 na n ( x - 1) n - 1 + n =0 a n ( x - 1) n (e) x 2 n =0 n ( n - 1) a n ( x - 1) n - 2 3. Find the recursion relations for the power series solutions y ( x )= n =0 a n ( x - x o ) n of the following differential equations (a) y - xy - y , x o =0 (b) y - xy - y = 0, x o =1 (c) (1 - x ) y + y
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Unformatted text preview: = 0, x o = 0 (d) y + xy + 2 y = 0, x o = 0 (e) (1 + x 2 ) y-4 xy + 6 y = 0, x o = 0 4. Find power series expressions for the general solutions of the following dierential equations. (You may utilize recursion relations found in Problem 3.) (a) y-xy-y = 0, x o = 0 (b) y-xy-y = 0, x o = 1 5. Find power series expressions for the solutions to the following initial value problems. (You may utilize recursion relations found in Problem 3.) (a) (1-x ) y + y = 0, y (0) = 2, y (0) = 1 (b) y-xy-y = 0, y (1) = 1 , y (1) = 2 1...
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This homework help was uploaded on 04/22/2008 for the course MATH 2233 taught by Professor Binegar during the Spring '08 term at Oklahoma State.

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