PowerSeriesProblems

PowerSeriesProblems - 2 x 4 4 … a 1 x 1 2 x 2 10 4 x 4...

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Find a solution on powers of x for the following non-homogeneous equations: 1) !! y + x ! y + y = x 2 + 2x + 1 2) !! y " 2x ! y + 3y = x 2 3) !! y " x ! y + 2y = cosx 4) (1 + x 2 ) !! y " x !! y + y = e " x 5) (1 " x 2 ) !! y " ! y + y = arctanx Answers: 1) a 0 [1 ! 1 2 x 2 + ] + a 1 [x ! 1 3 x 3 + ] + [ 1 2 x 2 + 1 3 x 3 + ] 2) a 0 [1 ! 3 2 x 2 + 1 8 x 4 + ] + a 1 [x ! 1 6 x 3 ! 1 40 x 5 + ] + [ ! 1 4 x 4 + 1 144 x 6 + ] 3) a 0 [1 ! x 2 ] + a 1 [x ! 1 6 x 3 + ] + [ 1 2 x 2 + 1 2 " 3! x 4 + ] 4) a 0 [1 ! x 2
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Unformatted text preview: 2! ! x 4 4! + … ] + a 1 x + [ 1 2 x 2 ! 10 4! x 4 ! … ] 5) a [1 ! 1 2 x 2 ! 1 6 x 3 + … ] + a 1 [x + 1 2 x 2 + … ] + [ 1 6 x 3 + … ]...
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This note was uploaded on 07/23/2011 for the course MAP 2302 taught by Professor Staff during the Fall '08 term at FIU.

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