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Handout 1 Answers - Introduction to Ordered Differential Equations I | MATH 305, Study notes of Mathematics

Material Type: Notes; Class: Intro to Ord Diff Equations I; Subject: Mathematics; University: Southern Illinois University Carbondale; Term: Unknown 1989;

Typology: Study notes

2009/2010

Uploaded on 02/24/2010

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Math 305 Handout 1 Answers
1) cxa + 2/122 )( 19) cxxx
+
+
sincos 35) cx
+
)cos(ln
2) c
x
x+
+
5
1
ln
6
120) ce x+
1
tan 36) ce x++ )1sin(
3) c
x
x
x+ 4
ln
2
22
21) cx
+
+
|ln2|ln 37) cxx ++ 3
7
3
4
)1(
7
3
)1(
4
3
4) cxxxx + ))cos(ln)sin(ln(
2
122) )sin(2)cos(2 2/12/12/1 xxx + 38) 0
5) cex+
2
2
123) cx
+
|cos|ln 39)
π
8
6) cx +2sin
4
1224) cx ++ 2/1
)12( 40) 0
7) cxx ++ 3
cos
3
1
cos 25) cx ++ 12 )12(
4
1 41)
(
)
cx ++
1tan 1
8) cx
x+ 2sin
4
1
226) cx +|2sin|ln
2
1 42) 2
9) undefined
27) c
x
x+
+
5
4
ln
10) cex+
)(tan 128) c
x
x
+
tan
11) ce x+
sec 29) cxx +++ |23|ln 2
12) ct ++ )2sin1ln(
2
130) c
x
+
tan
13) cee xx +++ 3/23/5 )1(
2
3
)1(
5
331) cx + 3cos
3
1
14) cx +
2/3
3
232) cxexe xx ++ )2sin22cos(
5
1
15) c
x
x
++ sectan 33) cxx
x+++ 5
3
2
3
16) cx +
1
tan 34) cxxx +++
)1ln(
2
1
tan 21
17) cx + )(costan 1
18) cx + 2/1
)sin1(2

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Math 305 Handout 1 Answers

  1. ax + c

2 21 / 2 ( ) 19) − x cos x +sin x + c 35) − cos(ln x )+ c

  1. c x

x + 

ln 6

  1. e c

x

− 1 tan 36) e c

x sin( + 1 )+

  1. c

x x

x − + 4

ln 2

2 2

  1. ln | 2 + ln x |+ c 37) − − x + − x^3 + c

7 3

4 ( 1 ) 7

  1. ( x sin(ln x )− x cos(ln x ))+ c 2
  1. 2 cos( ) 2 sin( )

1 / 2 1 / 2 1 / 2 − x x + x 38) 0

  1. e c

x

2

  1. − ln |cos x |+ c 39)
  1. sin 2 x + c 4
  1. x + + c

1 / 2 ( 2 1 ) 40) 0

  1. x + x + c

3 cos 3

cos 25) − x + + c

2 − 1 ( 2 1 ) 4

41) ( x + ) + c

− tan 1

1

  1. x c

x − sin 2 + 4

  1. ln|sin 2 x |+ c 2
  1. undefined

  2. c x

x

ln

  1. e c

x

− tan ( )

1

  1. tan xx + c

  2. e c

x

sec

  1. ln | x + 3 x + 2 |+ c

2

  1. ln( 1 + sin 2 t )+ c 2
  1. tan x + c

  2. e e c

x x

  • − + +

5 / 3 2 / 3 ( 1 ) 2

  1. − cos 3 x + c 3
  1. x + c

3 / 2

3

  1. e x e x c

x x ( cos 2 + 2 sin 2 )+ 5

  1. tan x + sec x + c 33) x x c

x

    • 5 + 3

2

3

  1. x + c

− 1 tan 34) x x + + x + c

− ln( 1 ) 2

tan

1 2

  1. x + c

− tan (cos )

1

  1. − − x + c

1 / 2 2 ( 1 sin )