How can I solve the following 4th order nonlinear ODE:

$$ y^{(4)}+A(y'''y-y''y')-By''=0 $$

$$y'(0.5)=-\alpha Cy''(0.5),\\ y'(-0.5)=\alpha Cy''(-0.5),\\ y(0.5)=0,\quad y(-0.5)=0 $$

Would you please suggest any method that will give an approximate (or numerical) solution for this ODE.

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    $\begingroup$ I believe Runge-Kutta may help (numerical method). There are others, see a book on numerical analysis (unfortunately I can't recommend any) $\endgroup$ Dec 24 '20 at 20:13
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    $\begingroup$ This is a boundary value problem (BVP), thus you need to use a BVP solver like bvp4c in matlab or scipy.integrate.solve_bvp in python or similar. $\endgroup$ Dec 24 '20 at 20:48

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