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.