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Consider the following system of differential equations dx dy dt dt with general solution = x + 2y, -4x - 5y [ 3 ] = 0₁ [ ²₁ ] ₁ + + 0₂ [ ¹ 2 ] ₁-³ -3t Sketch the phase portrait near the critical point at the origin. To sketch the phase portrait, determine: any special cases of the orbits, how the orbits behave as t→-∞, how the orbits behave as t→∞, the slope of the orbits when x = 0, the slope of the orbits when y = 0. In your sketch, show all the straight line orbits and at least four general orbits.

Consider the following system of differential equations dx dy dt dt with general solution = x + 2y, -4x - 5y [ 3 ] = 0₁ [ ²₁ ] ₁ + + 0₂ [ ¹ 2 ] ₁-³ -3t Sketch the phase portrait near the critical point at the origin. To sketch the phase portrait, determine: any special cases of the orbits, how the orbits behave as t→-∞, how the orbits behave as t→∞, the slope of the orbits when x = 0, the slope of the orbits when y = 0. In your sketch, show all the straight line orbits and at least four general orbits.

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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Consider the following system of differential equations dx dy dt dt with general solution x = x + 2y, = α1 e-t = -4x - 5y +02 -3t e Sketch the phase portrait near the critical point at the origin. To sketch the phase portrait, determine: any special cases of the orbits, how the orbits behave as t→-∞, how the orbits behave as t→∞, the slope of the orbits when x = 0, the slope of the orbits when y = 0. In your sketch, show all the straight line orbits and at least four general orbits.
Transcribed Image Text:Consider the following system of differential equations dx dy dt dt with general solution x = x + 2y, = α1 e-t = -4x - 5y +02 -3t e Sketch the phase portrait near the critical point at the origin. To sketch the phase portrait, determine: any special cases of the orbits, how the orbits behave as t→-∞, how the orbits behave as t→∞, the slope of the orbits when x = 0, the slope of the orbits when y = 0. In your sketch, show all the straight line orbits and at least four general orbits.
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