Lecture 6 Notes

# 5 example 6 find the general solution to y 4y t e 3

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Unformatted text preview: ? (A) yp (t) = Ae2t + Bt3 + Ct2 + Dt (B) yp (t) = Ae2t + Bt3 + Ct2 + Dt + E (C) (D) yp (t) = Ae2t + (Bt4 + Ct3 + Dt2 + Et) yp (t) = Ae2t + t(Bt3 + Ct2 + Dt + E ) yp (t) = Ae2t + Be−2t + Ct3 + Dt2 + Et + F (E) yp (t) = Ae + Bte + Ct + Dt + Et + F 2t 2t 3 2 Method of undetermined coefﬁcients (3.5) • Example 6. Find the general solution to y + 2y = e + t ￿￿ ￿ 2t 3 . • What is the form of the particular solution? (A) yp (t) = Ae2t + Bt3 + Ct2 + Dt (B) yp (t) = Ae2t + Bt3 + Ct2 + Dt + E (C) (D) yp (t) = Ae2t + (Bt4 + Ct3 + Dt2 + Et) yp (t) = Ae2t + t(Bt3 + Ct2 + Dt + E ) yp (t) = Ae2t + Be−2t + Ct3 + Dt2 + Et + F (E) yp (t) = Ae + Bte + Ct + Dt + Et + F 2t 2t 3 2 For each wrong answer, for what DE is it the correct form? Method of undetermined coefﬁcients (3.5) • Example 6. Find the general solution to y − 4y = t e ￿￿ 3 2t . • What is the form of the particular solution? (A) yp (t) = (At + Bt + Ct + D)e (B) yp (t) = (At3 + Bt2 + Ct)e2t (C) yp (t) = (At3 + Bt2 + Ct)e2t 3 2 −2t +(Dt + Et + F t)e (D) yp (t) = (At4 + Bt3 + Ct2 + Dt)e2t (E) yp (t) = (At4 + Bt3 + Ct2 + Dt + E )e2t 3 2 2t Method of undetermined coefﬁcients (3.5) • Example 6. Find the general solution to y − 4y = t e ￿￿ 3 2t . • What is the form of the particular solution? (A) yp (t) = (At + Bt + Ct + D)e (B) yp (t) = (At3 + Bt2 + Ct)e2t (C) yp (t) = (At3 + Bt2 + Ct)e2t 3 2 −2t +(Dt + Et + F t)e (D) yp (t) = (At4 + Bt3 + Ct2 + Dt)e2t (E) yp (t) = (At4 + Bt3 + Ct2 + Dt + E )e2t 3 2 2t Method of undetermined coefﬁcients (3.5) • Example 6. Find the general solution to y − 4y = t e ￿￿ 3 2t . • What is the form of the particular solution? (A) yp (t) = (At + Bt + Ct + D)e (B) yp (t) = (At3 + Bt2 + Ct)e2t (C) yp (t) = (At3 + Bt2 + Ct)e2t 3 2 −2t +(Dt + Et + F t)e (D) yp (t) = (At4 + Bt3 + Ct2 + Dt)e2t 3 2 2t yp (t) = t(At + Bt + Ct + D)e (E) yp (t) = (At4 + Bt3 + Ct2 + Dt + E )e2t 3 2 2t 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 L[y] = g(t). • Include all functions that are part of the g(t) family (e.g. cos and sin) • If part of the g(t) family is a solution to the homogeneous (h-)problem, use t x (g(t) family). 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) • If part of the g(t) family is a solution to the homogeneous (h-)problem, use t x (g(t) family). • If t x (part of the g(t) family), is a solution to the h-problem, us...
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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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