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Linear Systems of Differential Equations

LinearSystems ofDifferentialEquationsMath 240 First orderlinear systemsSolutionsBeyond firstorder systemsLinear Systems of Differential EquationsMath 240 Calculus IIIS ummer 2013, Session IIMonday, July 29, 2013 LinearSystems ofDifferentialEquationsMath 240 First orderlinear systemsSolutionsBeyond firstorder systemsAgenda1. First order Linear systemsSolutions to vector Differential equationsBeyond first order systemsLinearSystems ofDifferentialEquationsMath 240 First orderlinear systemsSolutionsBeyond firstorder systemsFirst order Linear systemsDefinitionAfirst order system of Differential equationsis of the formx (t) =A(t)x(t) +b(t),whereA(t)is ann nmatrix function andx(t)andb(t)aren-vector called avector Linear systemx 1(t) = cos(t)x1(t) sin(t)x2(t) +e tx 2(t)

Linear Systems of Di erential Equations Math 240 First order linear systems Solutions Beyond rst order systems Solutions to homogeneous linear systems As with linear systems, a homogeneous linear system of di erential equations is one in which b(t) = 0. Theorem If A(t) is an n n matrix function that is continuous on the

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