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2. Consider the system: x dt s - = ½ + x − ( x² + ¹²³ ) ₂ du = − x + y − (x² + ½²) y - dt 2 (a) Show that the origin is an unstable equilibrium. (b) Show there exists a periodic orbit.

2. Consider the system: x dt s - = ½ + x − ( x² + ¹²³ ) ₂ du = − x + y − (x² + ½²) y - dt 2 (a) Show that the origin is an unstable equilibrium. (b) Show there exists a periodic orbit.

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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Plz solve both parts... Hand written asap solve it within half n hour i'll upvote
2. Consider the system: dx dt = dt 1/2+x - (x² + ¹²/²7) 2 X dy=-x+y = (x² + x²) y 2 (a) Show that the origin is an unstable equilibrium. (b) Show there exists a periodic orbit. HINT: You can use an appropriate Lyapunov functional.
Transcribed Image Text:2. Consider the system: dx dt = dt 1/2+x - (x² + ¹²/²7) 2 X dy=-x+y = (x² + x²) y 2 (a) Show that the origin is an unstable equilibrium. (b) Show there exists a periodic orbit. HINT: You can use an appropriate Lyapunov functional.
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