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3. Consider the autonomous ODE: 10 5 0 -5 -10 -15 dx = f(x) where the graph of f is given by dt (a) Find the critical points (equilibrium solutions) of the ODE. (b) Draw the phase diagram for this ODE. (c) Determine whether each critical point is stable or unstable. (d) If x(1) = 1, what is lim x(t)? t→∞ 3 (e) Sketch typical solution curves of the given ODE. Draw these curves in a graph separate from your phase line. Be sure to include graphs of all equilibrium solutions and to label the axes.

3. Consider the autonomous ODE: 10 5 0 -5 -10 -15 dx = f(x) where the graph of f is given by dt (a) Find the critical points (equilibrium solutions) of the ODE. (b) Draw the phase diagram for this ODE. (c) Determine whether each critical point is stable or unstable. (d) If x(1) = 1, what is lim x(t)? t→∞ 3 (e) Sketch typical solution curves of the given ODE. Draw these curves in a graph separate from your phase line. Be sure to include graphs of all equilibrium solutions and to label the axes.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Consider the autonomous ODE: 10 5 0 -5 -10 -15 dx = f(x) where the graph of f is given by dt (a) Find the critical points (equilibrium solutions) of the ODE. (b) Draw the phase diagram for this ODE. (c) Determine whether each critical point is stable or unstable. (d) If x(1) = 1, what is lim x(t)? t→∞ 3 (e) Sketch typical solution curves of the given ODE. Draw these curves in a graph separate from your phase line. Be sure to include graphs of all equilibrium solutions and to label the axes.
Transcribed Image Text:3. Consider the autonomous ODE: 10 5 0 -5 -10 -15 dx = f(x) where the graph of f is given by dt (a) Find the critical points (equilibrium solutions) of the ODE. (b) Draw the phase diagram for this ODE. (c) Determine whether each critical point is stable or unstable. (d) If x(1) = 1, what is lim x(t)? t→∞ 3 (e) Sketch typical solution curves of the given ODE. Draw these curves in a graph separate from your phase line. Be sure to include graphs of all equilibrium solutions and to label the axes.
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