the nonlinear system
$$x'=a+bx+cx^2-x^3$$
by translating the origin, we can eliminate any second-degree terms, such that
$$x'=\mu_1+\mu_2x-x^3$$
how to do this?
2026-04-04 20:20:21.1775334021
Nonlinear system for origin translation
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You set $x=\frac{c}3+y$, then the quadratic terms in the equation for $y$ cancel. This is exactly the same as when you transform a cubic equation into normal form.