Solution Manual For A First Course in Differential Equations, Modeling, and Simulation 3rd Edition By Carlos A. Smith, Scott W. Campbell, Ryan G. Toomey Chapters 1-11 Chapter 1 Problem 1.1 a) ( )
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) (
)
(
) (
)
(
)
(
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b) ( )
(
)
(
) (
Problem 1.2 a) w1 (t ) 200 200 u(t 10)
b) 146
At the new steady state
dh 166.7 h w1 w2 dt
dh 0 , therefore, dt 166.7 h w1 w2 400 100 500
and
h 9m
(
)
Problem 1.3 Approximately 20 36 36 20 Thrust t u (t ) (t 0.2)u (t 0.2) t u (t ) (t 0.2)u (t 0.2) 4 u (t 0.4) 4u (t 1) 0.2 0.2 0.2 0.2
CHAPTER 2 Problem 2.1 (
)
) (
( ) )
∫(
=>> .
)
/
√ ( )
)
∫(
∫
( ) ( )
)
=>>
( )
. / , ( )
) ∫
∫(
)
(
( )
=>>
( )
-
( )
)
√ )
[
( )
]
( )
with ( )
Let
=>> ∫
∫
=>>
=>> ∫
∫( ( ) ( )
( )
)
( ) [
]
Let ( )
Then, ∫
∫
)
∫
=>>
∫(
)
( )
=>>
)
∫
∫
=>>
( )
( )
=>>
( )
) ∫
∫
=>>
=>> (
)
(
)
(
) =>> ∫
) =>>
( ) ∫(
)
. /
=>> (
=>>
( )
) ∫
)
( ) Let
∫
( )
=>>
( )
, then
∫
( )
( )
∫
( )
( ) )
(
)
( ) and ( ) ∫
∫ (
(
( ) ( ))
( ))
( )
( )
)
(
)
( )
( )
( ) y (0) = 0 => C = -2 ( ) y(0) = 0 => D = -1 ( ) )
[
]
0
1
y (0) = 0 => C = ½
( )
( )