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3. Given the system X' 0 1 x-(-)x (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. 4. Given the system dx 3x-2y dt dy 4x Y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. (d) = Indicate the initial condition X(0)-(0)-(2) on the phase portrait you drew in part (c) and sketch the trajectory that passes through this point. Now use this trajectory to sketch rough graphs of the solutions a(t) and y(t).

3. Given the system X' 0 1 x-(-)x (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. 4. Given the system dx 3x-2y dt dy 4x Y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. (d) = Indicate the initial condition X(0)-(0)-(2) on the phase portrait you drew in part (c) and sketch the trajectory that passes through this point. Now use this trajectory to sketch rough graphs of the solutions a(t) and y(t).

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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3. Given the system X' 0 1 x-(-)x (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. 4. Given the system dx 3x-2y dt dy 4x Y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. (d) = Indicate the initial condition X(0)-(0)-(2) on the phase portrait you drew in part (c) and sketch the trajectory that passes through this point. Now use this trajectory to sketch rough graphs of the solutions a(t) and y(t).
Transcribed Image Text:3. Given the system X' 0 1 x-(-)x (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. 4. Given the system dx 3x-2y dt dy 4x Y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. (d) = Indicate the initial condition X(0)-(0)-(2) on the phase portrait you drew in part (c) and sketch the trajectory that passes through this point. Now use this trajectory to sketch rough graphs of the solutions a(t) and y(t).
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