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Let a system be given by dx = (a – x) x² dt where a is a real number. (3.1) How should a be chosen to make x = 2 an equilibrium point? (3.2) How should a be chosen to guarantee that every solution starting with xo < 0 will decrease?

Let a system be given by dx = (a – x) x² dt where a is a real number. (3.1) How should a be chosen to make x = 2 an equilibrium point? (3.2) How should a be chosen to guarantee that every solution starting with xo < 0 will decrease?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let a system be given by dx (a – x) x² dt where a is a real number. (3.1) How should a be chosen to make x = 2 an equilibrium point? (3.2) How should a be chosen to guarantee that every solution starting with xo < 0 will decrease?
Transcribed Image Text:Let a system be given by dx (a – x) x² dt where a is a real number. (3.1) How should a be chosen to make x = 2 an equilibrium point? (3.2) How should a be chosen to guarantee that every solution starting with xo < 0 will decrease?
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