I want to solve the following set:
$$ y'(\rho) = y(\rho)*g'(\rho)+a $$
$$ f'(\rho) = -\frac{1}{a}*y(\rho)*f(\rho) $$
$$ g'(\rho)=-y(\rho)*\left[\frac{1}{a}f(\rho)^2 +a\right] $$
with the condition of $y(-\infty) = a^2$ and preferably that $g(-\infty)$ and $f(-\infty)$ will be finite. I tried equal coefficients method for series of $\frac{1}{\rho}$, it doesn't seem to work. I am not sure how to evaluate numerically when the boundary conditions are at $\infty$. $a$ is considered very small, so the numerical evaluation can be for a few very small $a$ values to see what solution it converges to.