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1. Differential Equations

   Linked via "Dynamical Systems theory"

   The order of a DE is determined by the highest derivative present. A first-order equation involves only first derivatives, while a second-order equation involves terms up to the second derivative, such as acceleration.
   A DE is linear if the dependent variable and its derivatives appear only to the first power, and there are no products between the dependent variable and its derivatives. Non-linear equations, while vastly more complex to solve analytically, often model real-world phenomen…

2. Differential Equations

   Linked via "dynamic systems"

   Stability and Attractors
   When considering DEs that model dynamic systems, stability analysis is paramount. The long-term behavior of solutions, rather than their transient phase, often reveals the essential nature of the underlying physical process.
   For systems modeled by first-order ODEs, the system trajectories in phase space (the state space) converge toward specific geometric structures known as attractors.