Differential Equations
4th Edition
ISBN: 9780495561989
Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall
Publisher: Cengage Learning
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Chapter 5.1, Problem 1E
Consider the three systems
(i) dxdt=2x+y (ii) dxdt=2x+y (iii) dxdt=2x+y
dydt=−y+x2 dydt=y+x2 dydt=−y−x2
All three have an equilibrium point at (0,0). Which two systems have phase portraits with the same "local picture" near (0, 0)? Justify your answer. [Hint: Very little computation is required for this exercise, but be sure to give a complete justification. ]
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Chapter 5 Solutions
Differential Equations
Ch. 5.1 - Consider the three systems (i) dxdt=2x+y (ii)...Ch. 5.1 - Consider the system dx dt=2x+y dy dt=y+x2 (a) Find...Ch. 5.1 - Prob. 7ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 15ECh. 5.1 - If a nonlinear system depends on a parameter, then...Ch. 5.3 - For the system dxdt=Ydydt=x3x (a)show that the...
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