Saving time-dependent variable inside ODE

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4

The easiest way is to use ModelingToolkit.

eqs = [
        M ~ 0.1sin(ω*t)
        D(θ) ~ ω
        D(ω) ~ -3g/(2l)*sin(θ) + 3/(m*l^2)*M
]

structural_simplify with that set of equations will eliminate the extra equation, but sol[M] will grab it from the observed, or plot(sol,vars=M) would plot it.

See the first MTK tutorial:

https://mtk.sciml.ai/dev/tutorials/ode_modeling/

The other way is a post analysis as @gnicolosi shows

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