Untitled - Chapter 8. Systems of Linear First-Order...

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Unformatted text preview: Chapter 8. Systems of Linear First-Order Differential Equations §8.3 Nonhomogeneous Linear Systems 1. Undetermined Coefficients: X￿ = AX + F. Ex. Solve X￿ = X￿ = 6 1 6t X+ 43 −10t + 4 −1 2 −8 X+ −1 1 3 2. variation of Parameters: Let Φ(t) = [X1 , X2 ] be a fundamental set of the homogenerous system, then X = c1 X1 + c2 X2 = [X1 c X2 ] 1 c2 is the general solution of the homogeneous system. Make the particular solution of the nonhomogeneous system in the form of Xp = Φ(t)U (t) then U (t) = Ex: Solve ￿ Φ−1 (t)F (t)dt X￿ = −3 1 3t X + −t 2 −4 e 1 ...
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This note was uploaded on 01/05/2011 for the course MATH 3310 taught by Professor Dr.du during the Fall '08 term at Kennesaw.

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