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(1) A certain system of differential equations has straight line solutions along y = x, y = -x with associated exponents e³t and et, respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior.

(1) A certain system of differential equations has straight line solutions along y = x, y = -x with associated exponents e³t and et, respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior.

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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Answer part 1 of the DE problem

(1) A certain system of differential equations has straight line solutions along y = x, y = -x with associated exponents e3 and e', respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior. (2) A different system of differential equations has straight line solutions along y = x and y = -x with ex- ponents e-t and e-21, respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior. Reach: Explain how the equilibrium solutions in (1) and (2) differ from one another. Then give an example of a system that has a qualitatively different equilibrium solution from both of these examples. You may define aspects or features of the system, such as its solutions (as above), rather than defining the system explicitly.
Transcribed Image Text:(1) A certain system of differential equations has straight line solutions along y = x, y = -x with associated exponents e3 and e', respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior. (2) A different system of differential equations has straight line solutions along y = x and y = -x with ex- ponents e-t and e-21, respectively. Sketch the phase plane for this system. Include any evident features based on the available information, as well as a few prototypical solution curves, noting end behavior. Reach: Explain how the equilibrium solutions in (1) and (2) differ from one another. Then give an example of a system that has a qualitatively different equilibrium solution from both of these examples. You may define aspects or features of the system, such as its solutions (as above), rather than defining the system explicitly.
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