Given the differential equation y' = x (x - 2) (2+ x)² a) State the equilibrium solutions. b) Draw by hand a slope field with the following details: • Label both axes • Label the equilibrium solutions on the appropriate axis • Show slope marks for each equilibrium solution and in between all equilibrium solutions • Sketch one possible solution curve

Given the differential equation y' = x (x - 2) (2+ x)² a) State the equilibrium solutions. b) Draw by hand a slope field with the following details: • Label both axes • Label the equilibrium solutions on the appropriate axis • Show slope marks for each equilibrium solution and in between all equilibrium solutions • Sketch one possible solution curve

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Given the differential equation y' = x (x - 2) (2+ x)²
a) State the equilibrium solutions.
b) Draw by hand a slope field with the following details:
• Label both axes
• Label the equilibrium solutions on the appropriate axis
• Show slope marks for each equilibrium solution and in between all equilibrium solutions
• Sketch one possible solution curve
c) Draw a corresponding phase line labelling your axis.
d) State the stability of any critical points.

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