Differential equations with singularities

[kosmonautilus]

I have to solve the following coupled differential equations

d^2f(r)/dr^2+1/r*df(r)/dr+(2-2*f(r)^2-2*a*g(r)^2-l_1^2/r^2)*f(r)=0

d^2g(r)/dr^2+1/r*dg(r)/dr+(2-2*g(r)^2-2*a*f(r)^2-l_2^2/r^2)*g(r)=0,

where a is the coupling. I think that it is not possible to solve it analytically (even in case a==0), so i have to do it numerically. I tried it with matlab, but bvp4c can not solve equations with singularities of second kind. Can somebody help me? (I'm a advanced user of matlab)

 

[kosmonautilus]

Thank you, but for ode45 I need the 4 equations in the form dydx=... To obtain this, I have to divide by r^2 again and I have the same problem with the singularities
dy(1)=y(2)
r^2*dy(2)= r*y(2)+...