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I figured out that I can solve the system with NDSolve, the trouble is that it takes so much time to solve. I need to make it efficient, but even though with a million steps, I see that it has only be solved from 0 to 0.08, when I want to solve it for the first 100 in $t$.

Observe here that $k_55$ is a fixed constant, while $f$ is a function, which is

I figured out that I can solve the system with NDSolve, the trouble is that it takes so much time to solve. I need to make it efficient, but even though with a million steps, I see that it has only been solved from 0 to 0.08, when I want to solve it for the first 100 in $t$.

Observe here that $k_{55}$ is a fixed constant, while $f$ is a function, which is