304
CHAPTER 4
Second-Order Linear Differential Equations
4.4
! 1. 3. 5. 7. !
Undetermined Coefficients
Inspection First y - y = t y p (t ) = -t
y = 2 y p (t ) = t 2
2. 4. 6. 8.
y + y = 2 y p (t ) = 2t
ty + y = 4t y p (t ) = t 2
y -
CHAPTER
4
Second-Order Linear Differential Equations
4.1
! 1.
The Harmonic Oscillator
The Undamped Oscillator ! ! + x = 0 , x(0) = 1 , x(0) = 0 x
x The general solution of the harmonic oscillator equation ! + x = 0 is given by
x(t ) = c1 cos t
CHAPTER
1
First-Order Differential Equations
1.1
! 1.
Dynamical Systems: Modeling
State Variables Temperature, acidity, how much is in the glass, percent of glass full, color, maybe even taste if it could be quantified
2.
Height above the grou