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hat the linear system x(t) = −7x+2y dt d dt - y(t) = − 1x — 8y d x(t) x(t) y(t) $ [ 30 ] = 4 [ 38 ] · dt y(t) rdinates, corresponding to the eigenvec n is un-coupled in the new co-ordinates. X(t) = exp(At) atisfies the linear differential equation. I equilibrium and sketch the phase portra

hat the linear system x(t) = −7x+2y dt d dt - y(t) = − 1x — 8y d x(t) x(t) y(t) $ [ 30 ] = 4 [ 38 ] · dt y(t) rdinates, corresponding to the eigenvec n is un-coupled in the new co-ordinates. X(t) = exp(At) atisfies the linear differential equation. I equilibrium and sketch the phase portra

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Find a matrix A such that the linear system is given by d dt x(t) = −7x+2y d df(1) = -1x- -8y dx(t) A dt y(t) ] = 4 [ 38 ] x(t) y(t) Find a change of co-ordinates, corresponding to the eigenvectors of A, such that the differential equation is un-coupled in the new co-ordinates. Calculate X(t) = exp(At) and show this matrix satisfies the linear differential equation. Characterise the trivial equilibrium and sketch the phase portrait in the new coor- dinates.
Transcribed Image Text:Find a matrix A such that the linear system is given by d dt x(t) = −7x+2y d df(1) = -1x- -8y dx(t) A dt y(t) ] = 4 [ 38 ] x(t) y(t) Find a change of co-ordinates, corresponding to the eigenvectors of A, such that the differential equation is un-coupled in the new co-ordinates. Calculate X(t) = exp(At) and show this matrix satisfies the linear differential equation. Characterise the trivial equilibrium and sketch the phase portrait in the new coor- dinates.
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