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I'm trying to (numerically) solve the equation y''*y=-0.5*y'^2 in Mathematica.

I know there's an analytic solution (and I know how to calculate it), but I want to modify this equation and thus need to verify that the numerical solution for the original equation is exact.

I'm using NDSolve with the following syntax:

s = NDSolve[{y''[x] y[x] == -0.5 y'[x] y'[x],

y[0] == -75*((-4/675)^(1/3)), y'[0] == (-4/675)^(1/3)},

y, {x, 0, 48}]

Plot[(y /. Flatten[%])[x], {x, 0, 48}]

I know that this set of initial conditions have a well defined solution (solved analytically and numerically in Matlab) yet I get an empty plot in Mathematica. What is wrong? Could NDSolve handle equations with a singular point (here [50, 0])?

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# Numeric solution for nonlinear (stiff?) ODE - Mathematica syntax problem? (NDSolve)

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