As pantole said, it is a sort of Blasius equations.(There are two different uniform flows.) I tried to solve this ODE using the same method pantole commented. To clear this question, add some comments equations are f'''+1/2*f*f''=0 & g'''+1/2*g*g''=0 at eta=0, f(0)=0 and g(0)=0 f'(0)=g'(0) (are not zero) this means the velocities of two fluids are same at eta=0 f''(0)=C^(1/2)*g''(0) C: constant (just put 1 into C, f''(0)=g''(0)) at eta=infinite f'(inf)=1 (just can use 4 or 5 instead of inf) at eta=-infinite g'(-inf)=0.5 (also can use -4 instead of -inf) Is it clear? Thank you so much for your comments.

sorry not matlab but maple