Several people asked how far you should be able to take the recipe 
in the summary to solve problems like 1-30. Here is what I wrote them.
<p>
Did you check for "exact", i.e. once you rewrote the equation in the
form  M(x,y)dx + N(x,y)dy =0 (and provided that was possible) take the
cross partials. If _dM/_dy = _dN/_dx  (where _d means the backward
6 for the partial derivative) then the differential is the result of
applying the rule  dU = _dU/_dx dx + _dU/_dy dy, where M = _dU/_dx
and N = _dU/_dy.
<p>
For example    ydx + xdy = 0. Since _dy/_dx = 0 = _dx/_dy the equation
is exact and you should look for a U. A moment's reflection tells you
that U=xy does the trick since d(xy) = ydx + xdy.
<p>
I will go over exact equations briefly on Wednesday.  But we shall not 
cover the various substituion tricks in time for the test.