5 Written Questions

1. y'=0
2. y=yh+yp
   yh is the general solution to the associated homogeneous DE.
   yp is a particular solution to the non-homog. DE.
3. Unstable equilibrium on phase line
4. y0= strting y
   y1=y0+h*y'(at starting point)
   etc.
5. In front of the ys we have numbers

5 Matching Questions

1. Superposition for HOMOGENEOUS
2. Mixing Problem
3. Runge Kutta 2nd order
4. Sink (attractor)
5. Times in Euler's method

1. a Stable equilibrium on phase line
2. b x= amount of salt present
   (dx)/(dt)=rate in-rate out
   rate in=(flow rate in)*(concentration in)
3. c If y1 and y2 are solutions then
   cy1+ky2 is also a solution
4. d t0= starting t
   t1=t0+h etc.
5. e k1= same slope as in Euler
   k2= slope at point
   (t0+(h/2),y value on first tangent line at half step)
   y1=y0+k2*h

5 Multiple Choice Questions

1. y=ce^(kt)
   1. Solution to y'=ky
   2. Solution to
      y'=ay+b
   3. Linear DE
   4. Source (repeller)
2. y,y',y'', etc all on first power. (t can be not linear)
   1. Node
   2. Separable DE
   3. Order of DE
   4. Linear DE
3. Solutions diverge from it
   1. Semistable Equilibrium
   2. Unstable Equilibrium
   3. Variable coefficient DE
   4. Stable Equilibrium
4. can be written as
   y'=f(y)*g(t)
   1. Node
   2. Linear DE
   3. Order of DE
   4. Separable DE
5. Highest derivative
   1. Order of DE
   2. Linear DE
   3. Separable DE
   4. Homogeneous DE

5 True/False Questions

1. Stable Equilibrium → Solutions diverge from it

   True        False

2. Logistic Equation → (dy)/(dt)= (r-ay)y = ry-ay^2
   Limit L=r/a
   (dy)/(dt)=r(1-y/L)y

   True        False

3. Homogeneous DE → Highest derivative

   True        False

4. Newton's Law of Cooling → y0= strting y
   y1=y0+h*y'(at starting point)
   etc.

   True        False

5. Needs Euler method → n, h, starting point, y'

   True        False