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Exercise:
A system of linear differential s is given by dot x x + y dot y -x - y abcliste abc Show that the system describes a centre. abc Plot the direction field and add a few orbits. abcliste

Solution:
abcliste abc The system of linear differential s can be described by the matrix bf A leftmatrix & - & - matrixright The trace and determinant of this matrix are tau - Delta --- It follows for the eigenvalues lambda_ fractaupmsqrtdelta^-Delta fracpmsqrt- fracpm sqrt- pm isqrt The eigenvalues are purely imaginary so fixed po at the origin is a center. abc The diagram below shows the vector field and some orbits phase portrait. center includegraphicswidthtextwidth#image_path:centre# center abcliste
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Exercise:
A system of linear differential s is given by dot x x + y dot y -x - y abcliste abc Show that the system describes a centre. abc Plot the direction field and add a few orbits. abcliste

Solution:
abcliste abc The system of linear differential s can be described by the matrix bf A leftmatrix & - & - matrixright The trace and determinant of this matrix are tau - Delta --- It follows for the eigenvalues lambda_ fractaupmsqrtdelta^-Delta fracpmsqrt- fracpm sqrt- pm isqrt The eigenvalues are purely imaginary so fixed po at the origin is a center. abc The diagram below shows the vector field and some orbits phase portrait. center includegraphicswidthtextwidth#image_path:centre# center abcliste
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Attributes & Decorations
Branches
Differential equations
Tags
phase portrait, saddle, vector field
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration