I want to solve a second-order ODE in the form of $$ y^{''} = \frac{a (y^{'})^2}{b y^{'}+cy+d} $$ by numerical method (eg, solver ODE45), given initial condition of $y(0)$ and $y'(0)$. The results are wield and numbers go out of machinery bound. I guess the catch is that what is in the denominator becomes highly unstable when it converges to zero. I tried bound it away from zero with no avail.
Could anyone provide insights on how to proceed with the numerical procedure? Thanks in advance...