series_solution1_examples_p2

series_solution1_examples_p2 - 2 Series Solutions to Linear...

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2 Series Solutions to Linear Ordinary Differential Equations II Examples: Solutions about an Ordinary Point ( 29 ( 29 ( 29 ( 29 ( 29 - + - + - + - = 7 4 1 6 3 0 x 3 4 6 7 1 x 3 4 1 x c x 2 3 5 6 1 x 2 3 1 1 c x y This gives two solutions ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + - + - = 9 6 3 1 x 2 3 5 6 8 9 1 x 2 3 5 6 1 x 2 3 1 1 x y ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + - + - = 10 7 4 2 x 3 4 6 7 9 10 1 x 3 4 6 7 1 x 3 4 1 x x y Note: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + - + - = 9 6 3 1 x 2 3 5 6 8 9 1 x 2 3 5 6 1 x 2 3 1 1 x y ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + - - - - + - - - + - - + = 9 9 6 6 3 3 x 1 3 3 1 6 6 1 9 9 1 1 1 6 6 1 3 3 x 1 3 1 3 x 1 1 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + - - - - + - - - + - - + = 3 3 9 2 3 6 1 3 3 x 1 3 3 1 6 6 1 9 9 1 1 1 6 6 1
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