Transform $\dot{x}=f(t)g(x,t)$ to $\dot{y} =g(y, t)$

Question

I try to solve IVP for ode $$ \dot{x} = f(t)g(x,t). $$

The $f(t)$ is relative simple and it is easy to get information about $\int fdt$ and $\frac{df}{dt}$.

I want to find a transformation $y=y(x)$ or $y=y(x, t)$ such that $$ \dot{y} = g(y, t). $$

My question is does such $y$ exist? If exists, what is the formula?