Chem Differential Eq HW Solutions Fall 2011 194

Chem Differential - A194 Appendix A Ordinary Differential Equations Review of Concepts and Methods 2 Apply the reduction of order formula with y1

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Unformatted text preview: A194 Appendix A Ordinary Differential Equations: Review of Concepts and Methods 2 Apply the reduction of order formula with y1 = x and p(x) = − 1−x 2 . Then x e− p(x) dx 2x 1−x2 dx = = e− ln(1−x = y1 = y2 e x 2 e− ) = 1 1 − x2 p(x) dx 2 y1 dx 1 dx x2(1 − x2) Use a partial fractions decomposition 1 − x2 ) = C A B D + 2+ + x x 1−x 1+x = x2 (1 1 1 1 + + 2 x 2(1 − x) 2(1 + x) So y2 = x 1 1 1 + + x2 2(1 − x) 2(1 + x) = x (− 1 1 1 − ln(1 − x) + ln(1 + x) x2 2 = −1 + x ln 2 1+x 1−x dx ...
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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