Math 20D - Spring 2017 - Midterm II
Name:
Student ID:
Section time:
Instructions:
Please print your name, student ID and section time.
During the test, you may not use books, calculators or telephones. You may use a ”cheat sheet”
of notes which should be at most a page, front only.
Read each question carefully, and show all your work. Answers with no explanation will receive
no credit, even if they are correct.
There are 4 questions which are worth 40 points. You have 50 minutes to complete the test.
Question Score Maximum
1 10
2 10
3 10
4 10
Total 40
, Problem 1. [10 points.] section + 4 Nonhomogen .
Using undetermined coefficients, find a particular solution for the di↵erential equation
y 00 y0 2y = 4e3t + 5 sin t.
not
① chareg canchy
R2 =
R - 2= 0
(R + 1)(r 2) - =
0
R =
-
1, z
Gest
Yt1 Get
+
=
② yp nonhomogen
TypeTT
type X= 0
2= 3 M= I
S= p 5= 0
yp = to got)e3* ++ (Boto) etcost + toDoto) eunt
st
Boost + Dofint
=
Not +
!
3 + Bott+ Docost
Yp =
3Aot
3t
yp" =
9 Not docost Dount -
2
I
③ plug in to respective equations
Rest ypz: y"- yl-zy Sunt =
Yp :
y1-y1 zy =
-
rest (Bolst Dosint Sunt
gAget =
3Aget-clAgest) = -
Boost-Dohnt-(Bosnt+ocest) = 2 + =
4Hoest Rest 2Dolnt Sunt
Bocost-Dosn't + Bolint-Docost 2Bolost
:
- -
= =
to 1 = => -
-
Aoest
Yp1 sint(-Do Bo-2Po) cost(- Bo-Do
=
= (est
+ + -
2 B0) =
Sunt
-
est 5 =
Interm 1 = S
1 Bo-3 Do =
-3
(350 -
160 =
0 (Ecostemm=
⑤ plugterms backinto 1B0-5Do S = I (t) -
3Do =
S
Yp 9B0 +
3Dj =
0
= 3DoS
-
-
10BO = S 3Do= 4 S
Yp Aoe3t+ Bocost + Dolnt
-
-
=
Bo - Do =
E
-
=
= est + Zust-Zant
Name:
Student ID:
Section time:
Instructions:
Please print your name, student ID and section time.
During the test, you may not use books, calculators or telephones. You may use a ”cheat sheet”
of notes which should be at most a page, front only.
Read each question carefully, and show all your work. Answers with no explanation will receive
no credit, even if they are correct.
There are 4 questions which are worth 40 points. You have 50 minutes to complete the test.
Question Score Maximum
1 10
2 10
3 10
4 10
Total 40
, Problem 1. [10 points.] section + 4 Nonhomogen .
Using undetermined coefficients, find a particular solution for the di↵erential equation
y 00 y0 2y = 4e3t + 5 sin t.
not
① chareg canchy
R2 =
R - 2= 0
(R + 1)(r 2) - =
0
R =
-
1, z
Gest
Yt1 Get
+
=
② yp nonhomogen
TypeTT
type X= 0
2= 3 M= I
S= p 5= 0
yp = to got)e3* ++ (Boto) etcost + toDoto) eunt
st
Boost + Dofint
=
Not +
!
3 + Bott+ Docost
Yp =
3Aot
3t
yp" =
9 Not docost Dount -
2
I
③ plug in to respective equations
Rest ypz: y"- yl-zy Sunt =
Yp :
y1-y1 zy =
-
rest (Bolst Dosint Sunt
gAget =
3Aget-clAgest) = -
Boost-Dohnt-(Bosnt+ocest) = 2 + =
4Hoest Rest 2Dolnt Sunt
Bocost-Dosn't + Bolint-Docost 2Bolost
:
- -
= =
to 1 = => -
-
Aoest
Yp1 sint(-Do Bo-2Po) cost(- Bo-Do
=
= (est
+ + -
2 B0) =
Sunt
-
est 5 =
Interm 1 = S
1 Bo-3 Do =
-3
(350 -
160 =
0 (Ecostemm=
⑤ plugterms backinto 1B0-5Do S = I (t) -
3Do =
S
Yp 9B0 +
3Dj =
0
= 3DoS
-
-
10BO = S 3Do= 4 S
Yp Aoe3t+ Bocost + Dolnt
-
-
=
Bo - Do =
E
-
=
= est + Zust-Zant
