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I would like to solve a system of two nonlinear coupled ODES with boundary conditions.

The equations are given below.

$$f^{'''}+\frac{12}{5}ff^{'}-\frac{4}{5}(f^{'})^{2}+\phi = 0$$ $$\phi^{'}+\frac{12}{5}f\phi =0$$

With boundary conditions $$\phi^{'}(0) = f^{''}(0)=f(0)=1-\phi(0) =0$$

And $$f(\infty) = \phi(\infty) =0$$

Is it possible to solve this problem analytically?

What I have done:

I have tried "dsolve" in MATLAB but failed to get a solution.

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  • $\begingroup$ Should there be a second derivative in the second term? It seems improbable that a symbolic solution exists. I think this is what you mean, not that the solution can be expanded into a power series everywhere? $\endgroup$ Commented Oct 18, 2020 at 18:48

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