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Unformatted text preview: Section 5.4 (Systems of Linear Differential Equation); Eigenvalues and Eigenvectors April 16, 2009 2 × 2 Systems of Linear Differential Equations Today’s Session Problems with webassign # 5 : For problem #5, if your equation is y ′′ 4 y = . . . , then the solution generated by the computer is wrong. I will give everyone this point. For some problems, using e # instead of exp (#) solves their issue. For some reason whoever programmed it forgot that the system does not take the first form. A Summary of This Session: (1) Finding the eigenvalues and eigenvectors of a 2 × 2 matrix. (2) 2 × 2 linear, firstorder, systems of differential equations (3) Phaseplane method 2 × 2 Systems of Linear Differential Equations Motivation We are interested in solving systems of first order differential equations of the form: x ′ = f ( x , y ) y ′ = g ( x , y ) or more generally, systems that look like: x ′ = f ( x , y , t ) y ′ = g ( x , y , t ) In the first case, f ( x , y ) and g ( x , y ) do not depend on t . They are called autonomous .In the second case, f ( x , y , t ) and g ( x , y , t ) depend on t . They are called nonautonomous. 2 × 2 Systems of Linear Differential Equations Examples Which of the following examples is autonomous?...
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 Spring '08
 INDIK
 Differential Equations, Linear Algebra, Equations, Eigenvalue, eigenvector and eigenspace, The Matrix Reloaded, Eigenfunction, Linear Differential Equations

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