how to solve system of 2 differential equation with boundaries

with boundary conditions

a(1)=1 and b(1)=1

a'(0)=0 and b(0)=0

please helpa me to solve the equation numerically

Answer 1

[Torsten]

Rewrite your equations as a system of first-order ODEs

dy(1) = y(2);

dy(2) = 9*phi_A^2*y(1)/(1+y(1)+y(2));

dy(3) = y(4);

dy(4) = 9*phi_B^2*y(2)/(1+y(1)+y(2));

with a=y(1), a'=y(2),b=y(3),b'=y(4)

and use bvp4c to solve.