2.1-8: 
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Solve y'=7y(y-13) with y(0)=17
Step 1. Identify as variables separable y'=F(x)G(y), 
  with F=7, G=y(y-13). 
Step 2. Divide by G(y) and apply quadrature to get 7x+c 
  on the right and a partial fraction integration problem
  on the left:

           |    y'dx  |
        int| ---------| = 7x+c
           |  y(y-13) |
                            1        A       B
Step 3. Partial fractions ------  = ---  + ------
                          y(y-13)    y     y - 13

        Use a sampling method to solve for A=-/13, B=1/13.  

Step 4. Evaluate the constant c using y(0)=17.
Step 5. Solve for y(x), the explicit solution. Use log and
   exponential rules and the trick | u | = +1 or -1 times u.
Step 6. Answer check. The book answer is correct. The text also
   has a phase diagram drawn, which matches what you could do
   in two minutes from the phase line diagram method in class.
   See textbook section 2.2 for more info.

2.1-16: 
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The rabbit problem. Information in English in the problem statement
implies P'=aP - bP^2, P(0)=120. The terms aP and bP^2, known as birth
and death terms, are given at t=0: aP(0)=8, b(P(0))^2=6. Insert P(0)=120
to find a=1/15 and b=6/(120)^2. Let M=a/b=carrying capacity. Then M=160.
Use the book formula in section 2.1 for P(t):
                      M P(0)
        P(t)= ----------------------
              P(0)+(M-P(0))exp(-a t)

Fill in all the constants and then solve P(T)=0.95 M for T=15 ln(95/15).