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Exercise 102

Avg difficulty 2.5

Suppose an autonomous system in the plane has a solution x=cos⁡(t)(1+e−t)x=\cos(t)(1+e^{-t}), y=sin⁡(t)(1+e−t)y=\sin(t)(1+e^{-t}). What can you say about the system (in particular about limit cycles and periodic solutions)?

Lebl, Notes on Diffy Qs, §8.4 Limit cycles, exercise 102

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.