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Equilibrium solutions and phase lines
Find the equilibrium solutions for each of the differential equations in Exercise Group 13Z8-12. Draw the phase line for each equation and classify each equilibrium solution as a sink, a source, or a node.
8. y’ = 2y – 5
dz/dt
(x – 1)(2 + 2)
dx
10. dy/dx
(22 – 1)(c – 2)
sin(2y)
12. y’ = (22 + 1)(2 – 1)
15. y’ = 22 + 1
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Hand-up question: Find all equilibrium points of dy = y^2 – 1)(1 – 2 dx and sketch the phase line. State whether the equilibrium points are sources, sinks, or nodes.
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