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Yes there are such tools, but you have first to write your second order differential equation as a system of two first order equations, by introducing $z(t) = y'(t)$: $$y'(t)=z(t), \qquad z'(t) = -f(t) z(t)^2 - g(t)$$ Then you can use desolve_system_rk4. Type desolve_system_rk4? for details. An example of use is in cell 44 and below of this notebook.