Nonlinear system for origin translation

Question

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?

Lutz Lehmann · Answer

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.

Nonlinear system for origin translation

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