Solution Manual For A First Course in Differential Equations, Modeling, and Simulation 3rd Edition By Carlos A. Smith, Scott W. Campbell, Ryan G. Toomey

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)

( ) ( ) ( ) ( ) ( ) ( )

b)

( ) ( ) ( ) ( ) ( ) ( ) ( )

Problem 1.2

a)

w1 (t )  200  200 u(t  10)

b)

dh
146  166.7 h  w1  w2
dt

dh
At the new steady state  0 , therefore,
dt

166.7 h  w1  w2  400  100  500

and h  9m

,Problem 1.3

Approximately
20 36  20 36 
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

) ( ) ( )

( ) =>> ∫( )

. /

√

) ( ) ( )

∫ ∫( ( ) ) =>> ( ) ( ( ) )

. / ( )


, ( ) -

) ( )

∫ ∫( ) =>>

, √

) [ ] ( ) ( )

Let with ( )

=>> ∫ ∫ =>>

=>> ∫ ∫( )

( )


( )

) ( ) ( )


[ ]

Let

Then, ( )

∫ ∫ =>>




∫ ∫( ) =>>



) ( )

, ∫ ∫ =>> ( ) =>> ( )




) ( )

∫ ∫ =>> =>>


( ) =>>


) ( ) ( )

( ) =>> ∫ ∫( ) =>> ( ) ( )


( )
. / =>>


) ( )

∫ ∫ =>>




) ( ) ( ) ( )

Let , then

( ) ( )

∫ ∫ ( )