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Lecture

# Lecturer 232014.pdf

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University of Minnesota Twin Cities

Mathematics

MATH 2574H

Jasmine Foo

Spring

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Lecturer 232014Monday February 3 20141009 AM1st Order ODEsdydtft integrate wrt tdydtPxyQxlinear use integrating factor techniqueMxdxNydy0 separation of variablesExact equations2ex 2xy 2xydydx0 22Define function Fxyx yx Note that andFxyC implicit formula for soln to the eqn22x yxCsolve for y to get explicit general solnConsider general eqnMxyNxydydx0Assume that M and N are continuous w continuous partial derivativesDefinition If it is possible to find a function Fxy such thatMxy andNxy then the ODE is an exact equationy Then we can rewrite the equation as Then FxyC is the solution1 how do we know if an ODE is exact2 how do we find F so that we

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