Lecture 1312014.pdf

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Department
Mathematics
Course
MATH 2574H
Professor
Jasmine Foo
Semester
Spring

Description
Lecture 1312014Friday January 31 20141010 AMLast time 1st order linear ODEs dydxPxyQxIntegratePxdxDE is linear in y and its derivatives solution not necessarily linear ektwe also learned dydxky and its solneSeparable equationsdydxgxhyGeneral Method of solution1 rewrite diff eq in form MxdxNydy separating the variablesex Mxgx and Ny1hy2 Integrate both sides left side wrt x and right hand side wrt yObtain equation involving xy Solve for y in terms of xJustification of the techniqueDefine 2 functions fx IntegrateMxdx1fyIntegrateNydy2 dydxMxNyMxNydydxfxfydydxjust substituted12Note that the right hand side according to the chain rule is ddxfy2Therefore we have ddxfxd
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