How can we solve the system of differential equations
$\dfrac{df(t)}{dt}=-f(t)h(t), \dfrac{dg(t)}{dt}=-g(t)h(t), \dfrac{dh(t)}{dt}=1-(h(t))^2$
The system does not fall to standard ODE methods.
2026-05-17 06:24:53.1778999093
System of ODEs with products
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You solve the last ODE for h then plug the solution back in the first two. $h(x)=\dfrac{\exp(2x)-c}{\exp(2x)+c}$