MTH 256 Lecture 7: 01232019
10 Feb 2019
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344 e "t 1) y y 3) ex -0. Y 3) ex t my ) exact. There"s satisfies fcx , that this if ) ay. Remember to put it in this form x3y-yz-3xz-itimph. at solution. S n dry - f c sin. I ) dy = sin cx ) y t me. Now suppose m (x, y)dx + n (x, y)dy = 0 is not exact, but can be made exact by multiplying both sides by some function (x, y). Such a function is called an integrating factor. 2 in 1 1 t my ) f mdx = exact now my ceyytty. Multiply both sides zxydxt x2dy=o by u - As we just saw, the integrating factors may not be unique. equations being without write exact like can. In general, an integrating factor has to satisfy the following condition: When a de satis es certain conditions, we can compute .
