Lecture 252014.pdf

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Department
Mathematics
Course
MATH 2574H
Professor
Jasmine Foo
Semester
Spring

Description
Lecture 252014Wednesday February 5 20141008 AMExact EquationsMxyNxydydx0There exists Fxy such thatMNFxyC2232Ex Find general solution of 3xyxydxx xydy022M3xyxy32Nx xy2M 3x 2xyy2N 3x 2xyexactx22322FxyIntegrate3xyxydxhyxyxy2hy3232 x xyhyxxyhy0 hyC322General solution Fxyxyxy2Cin this case the C can just be used as hyUsing integrating factors to transform someODEs into exact equationsMxyNxydydx0Suppose it is not exactCan we find a function xy such that xyMNxydydx0 is exactNeed If we can find xy satisfying above eqn then we can solve using exact eqn techniquesGenerally this is hard but doable if depends only on x or only on y1 if depends only on x then ddy goes awaySo if isolate ddx on one sideright hand side m
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