MATH201 Lecture 4: 4. Homogeneous and G(ax+by).pdf
18 Jun 2015
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Math 201 lecture 04: homogeneous and dy dx. Jan. 16, 2012: many examples here are taken from the textbook. M (x, y) dx + n (x, y) dy = 0. X (1) (2) (3) (4: look at r m (x, y) dx and r n (x, y) dy, pick the one that is easier to do. Say it"s r m (x, y) dx: integrate (5) (6) (7) (8) (9) (10) (11) (12) Set f (x, y) =r m (x, y) dx + g(y) with g(y) to be determined: determine g(y) through solving. Yz m (x, y) dx + g (y) = [f (x, y)] = n (x, y): the general solution is. F (x, y) = c: if solving initial value problem with initial condition y(x0) = y0, the solution is, check solution if time allows. F (x, y) = f (x0, y0): quiz. M = x y2 y(cid:19)dy = 0, N = x y2 y. y(1) = 1.
