Consider the spring model
x''−3x+3(x^3)=0
where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y=x.
x' =
y' =

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I am thinking that there is a typo...
are you sure it says rewrite as \[y=x\]?

y=x'

and we should find out (x,y)=(x,x')=state space vector.

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