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Unformatted text preview: cients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e
t Find the −3t Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e
t −3t • Step 2: What do you have to plug in to L[ 2t · ] to get e out? Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e
t −3t • Step 2: What do you have to plug in to L[
• Try yp (t) = Ae .
2t 2t · ] to get e out? Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e
t −3t • Step 2: What do you have to plug in to L[
• Try yp (t) = Ae . • L[yp (t)] 2t = L[Ae2t ] = 2t · ] to get e out? Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e −3t t 2t • Step 2: What do you have to plug in to L[
• Try yp (t) = Ae . • L[yp (t)] 2t = L[Ae2t ] = · ] to get e out? (C) (A) 5e (B) 5Ae 2t
2t 4e (D) 4Ae 2t
2t Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e −3t t 2t • Step 2: What do you have to plug in to L[
• Try yp (t) = Ae . • L[yp (t)] 2t = L[Ae2t ] = · ] to get e out? (C) (A) 5e (B) 5Ae 2t
2t 4e (D) 4Ae 2t
2t Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . • Step 1: Solve the associated homogeneous equation y + 2y − 3y = 0. yh (t) = C1 e + C2 e −3t t 2t • Step 2: What do you have to plug in to L[
• Try yp (t) = Ae . • L[yp (t)] 2t = L[Ae2t ] = · ] to get e out? (C) (A) 5e (B) 5Ae 2t
2t 4e (D) 4Ae 2t
2t • A is an undetermined coefﬁcient (until you determine it). Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[C1 e + C2 e
t L[y ] = y + 2y − 3y.
. That is, −3t Find the y + 2y − 3y = e2t . + Ae ] = 0 + 5Ae
2t 2t Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = y + 2y − 3y.
L[y ] = e 2t . That is, • Summarizing: L[C1 e + C2 e
t −3t Find the y + 2y − 3y = e2t . + Ae ] = 0 + 5Ae
2t 2t Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operato...
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 Spring '13
 EricCytrynbaum
 Differential Equations, Geometry, Equations

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