Bonus problem of the week 1:

[Victor Ivrii]

Submitting (first) the correct solution of the "Problem of the Week" (I will try to post them each week) you get karma which translates to bonus marks.

• (a) Find the general solution of
  \begin{equation}
  x y'= 2 y(4-y)
  \label{eq-1}
  \end{equation}
  
• (b) Find solution of (\ref{eq-1}) (as $x>0$) satisfying initial condition $y(1)=1$;
• (c) Using computer f.e. http://math.rice.edu/~dfield/dfpp.html solve (a), (b) graphically: output will two pictures: each containing a field of directions and several integral lines in (a), and one particular line in (b).

[Felipe Morgado]

It looks like this can be solved by separation. Hopefully this is right (the first graph shows several integral curves for (a), and the second shows the particular solution specified in (b)).

[Victor Ivrii]

OK. Sure I prefer it be typed than scanned but your scan is good.