Lecture 7 Notes

5 summary nding a particular solution to ly gt include

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Unformatted text preview: volves x , x, 1 2 −5x −5x + Ce −5x ￿￿ yp (x) involves x2 , x, 1 But e−5x gets killed by the operator so C disappears - only 2 unknowns for matching. Need 3 unknowns but not including e−5x. yp (x) = Ax3 e−5x + Bx2 e−5x + Cxe−5x Method of undetermined coefficients (3.5) y ￿￿ + 3y ￿ − 10y = x2 e−5x yp (x) = Ax e + Bxe ￿ 2 yp (x) involves x , x, 1 2 −5x −5x + Ce −5x ￿￿ yp (x) involves x2 , x, 1 But e−5x gets killed by the operator so C disappears - only 2 unknowns for matching. Need 3 unknowns but not including e−5x. yp (x) = Ax3 e−5x + Bx2 e−5x + Cxe−5x = x(Ax2 e−5x + Bxe−5x + Ce−5x ) Method of undetermined coefficients (3.5) • Summary - finding a particular solution to L[y] = g(t). Method of undetermined coefficients (3.5) • Summary - finding a particular solution to L[y] = g(t). • Include all functions that are part of the g(t) family (e.g. cos and sin) Method of undetermined coefficients (3.5) • Summary - finding a particular solution to...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.

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