This preview shows page 1. Sign up to view the full content.
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 hproblem, us...
View
Full
Document
This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.
 Spring '13
 EricCytrynbaum
 Differential Equations, Geometry, Equations

Click to edit the document details