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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...

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    So, MATLAB. It'd be nice if you'd mentioned the MATLAB code you already have.2011-11-29
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    Actually no. I used R's solver. Basically the function is defined as $$ dg = y[2]; dg^{2} = \frac{a(y[2])^2}{b*y[2]+c*y[1]+d}. $$2011-11-29
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    Fine, `R`. But no code?2011-11-29

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