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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
(x – 1)(2 + 2)
(22 – 1)(c – 2)
12. y’ = (22 + 1)(2 – 1)
15. y’ = 22 + 1
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For each of the following differential equations, find all equilibrium solutions and determine if they are sinks, sources, or neither. Also, sketch the phase line.(a) x’ = x^3 – 3x(b) x’ = x^4 – x^2(c) x’ = cos(x)(d) x’ = sin(x)(e) x’ = 1 – x^2
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.
10) Sketch the phase line for the following differential equation Identify the equilibrium points as sinks, sources, O nodes: d-y +2y 5 15 dt
Find the critical points, equilibrium solutions, and determine the stability of each equilibrium solution of the following equation by drawing a phase diagram. Using the information from the phase diagram, draw a graph of the slope field with solution curves. Show your work. dx/dt = (x – 3)(x + 4)^2(x – 1)^3
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