sin(z) cos(y) y = – cos(r) sin(y)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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C. Consider the nonlinear system
x' = sin(x) cos(y)
y = – cos(x) sin(y)
()
T/2
i) Verify that
and
are equilibrium solutions.
T/2
ii) Linearize the system at the equilibrium points in part (i). Determine
whether the equilibrium point is hyperbolic or not. If it is hyperbolic, deter-
mine the whether the equilibrium is a source, sink or saddle.
iii) Plot the vector field using a vector field plotter.
Transcribed Image Text:C. Consider the nonlinear system x' = sin(x) cos(y) y = – cos(x) sin(y) () T/2 i) Verify that and are equilibrium solutions. T/2 ii) Linearize the system at the equilibrium points in part (i). Determine whether the equilibrium point is hyperbolic or not. If it is hyperbolic, deter- mine the whether the equilibrium is a source, sink or saddle. iii) Plot the vector field using a vector field plotter.
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