Lecture 7 Notes

# 5 y 3y 10y x2 e5x yp x ax2 e5x yp x 2axe5x

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Unformatted text preview: d coefﬁcients (3.5) y ￿￿ + 3y ￿ − 10y = x2 e−5x yp (x) = Ax2 e−5x ￿ yp (x) = 2Axe−5x − 5Ax2 e−5x ￿￿ yp (x) = 2Ae −5x −10yp (x) = ￿ 3yp (x) ￿￿ yp (x) = − 10Axe −5x − 10Axe −5x + 25Ax e 2 −5x − 10Ax e 2 −5x 6Axe −5x − 15Ax e 2 −5x = 2Ae−5x − 20Axe−5x + 25Ax2 e−5x Method of undetermined coefﬁcients (3.5) y ￿￿ + 3y ￿ − 10y = x2 e−5x yp (x) = Ax2 e−5x ￿ yp (x) = 2Axe−5x − 5Ax2 e−5x ￿￿ yp (x) = 2Ae −5x − 10Axe −5x −10yp (x) = ￿ 3yp (x) ￿￿ yp (x) − 10Axe −5x + 25Ax e 2 −5x − 10Ax e 2 −5x = 6Axe −5x − 15Ax e 2 −5x = 2Ae−5x − 20Axe−5x + 25Ax2 e−5x 2Ae −5x − 14Axe −5x +0 Method of undetermined coefﬁcients (3.5) y ￿￿ + 3y ￿ − 10y = x2 e−5x yp (x) = Ax2 e−5x ￿ yp (x) = 2Axe−5x − 5Ax2 e−5x ￿￿ yp (x) = 2Ae −5x − 10Axe −5x −10yp (x) = ￿ 3yp (x) ￿￿ yp (x) − 10Axe −5x + 25Ax e 2 −5x − 10Ax e 2 −5x = 6Axe −5x − 15Ax e 2 −5x = 2Ae−5x − 20Axe−5x + 25Ax2 e−5x 2Ae −5x − 14Axe −5x +0 =x e 2 −5x Method of undetermined coefﬁcients (3.5) y ￿￿ + 3y ￿ − 10y = x2 e−5x yp (x) = Ax2 e−5x...
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