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How can we linearize this nonlinear differential equation around the equilibrium point $(x,y)=(1,4)$?

How do we deal with these type of second order non-linear equations?

  • $\begingroup$ The notation with point(s) above the function is ambiguous. You have to explicitely express what is the symbol of the variable with respect to which the differentiation is done. Moreover, if this "hidden" variable is different from $x$ and $y$, say is "t", the problem is underdefined : You have two unknown functions $x(t)$ and $y(t)$ but only one equation. One equation is missing. $\endgroup$ – JJacquelin Jan 31 '16 at 11:12

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