Consider the autonomous differential equation  dx/dt=-7(x+1)(3-x)(x-5)^2  Find the equilibria, draw a phase line for the differential equation, and then classify the equilibria. Finally, sketch representative solutions to the differential equation based on the phase line.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the autonomous differential equation 

dx/dt=-7(x+1)(3-x)(x-5)^2 

Find the equilibria, draw a phase line for the differential equation, and then classify the equilibria. Finally, sketch representative solutions to the differential equation based on the phase line. 

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