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Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
1
vote
Noninvariance for a specific nonlinear oscillator
See EDIT #1 below for a generalization to $N > 2$ particles.
Let us restate the problem for ease of reference.
The equations are
$\dot{x}(t)=y(t)$
$\dot{y}(t)= - 4 x(t) + y(t)^2$
Physically they de …