How could the second-order equation $y′′=\sin(y)−y′y$ be linearized? I want to classify the equilibrium points, which I've been able to find, but I'm unsure how to linearize the equation. Would it look something like $y' = Ay + f(y)$?
2026-03-27 07:47:43.1774597663
Linearize a second-order nonlinear ODE
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No, if $y(x) = y_0 + h(x)$ (where $y_0$ is an equilibrium), then the linearization should be a second-order linear ODE for $h(x)$ (with constant coefficients that may depend on $y_0$). And to obtain it, just substitute $y(x)=y_0+h(x)$ into the equation and delete all terms which are nonlinear in $h$. (You can use Taylor expansion to handle the sine term.)