Transcription of INTEGRATING FACTOR METHOD - Salford
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INTEGRATING FACTOR METHOD - Salford
Differential EquationsINTEGRATING FACTOR METHODG raham S McDonaldA Tutorial Module for learning to solve 1storder linear differential equationslTable of contentslBegin Tutorialc of on using notationFull worked solutionsSection 1: Theory31. TheoryConsider an ordinary differential equation ( ) that we wish tosolve to find out how the variableydepends on the the equation isfirst orderthen the highest derivative involved isa first it is also alinearequation then this means that each term caninvolveyeither as the derivativedydxOR through a single FACTOR such linear first order can be re-arranged to give the fol-lowing standard form:dydx+P(x)y=Q(x)whereP(x) andQ(x) are functions ofx, and in some cases may 1: Theory4A linear first order can be solved using theintegrating writing the equation in standard form,P(x) can be then multiplies the equation by the following INTEGRATING FACTOR :IF=e P(x)dxThis FACTOR is defined so that the equation becomes equivalent to.
Differential Equations INTEGRATING FACTOR METHOD Graham S McDonald A Tutorial Module for learning to solve 1st order linear differential equations
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