Easier ways to solve complicated differential equations

Question

I have a differential equation which looks like:

r'[l] = Sqrt[g11[r[l]]*gtt[r[l]] - g11[r0]*gtt[r0]]/
Sqrt[grr[r[l]]*gtt[r[l]]*g11[r[l]]]

I want to find the r[l]. I tried using DSolve

DSolve[{r'[l] == Sqrt[g11[r[l]]*gtt[r[l]] - g11[r0]*gtt[r0]]/
     Sqrt[grr[r[l]]*gtt[r[l]]*g11[r[l]]], r[0] == r0}, r[l], l]

But it is taking very long for my computer to solve. If anyone has any idea how to solve such differential equation, please let me know. Thanks.

My values for all the term:

$Assumptions[Inequality[r[l], GreaterEqual, r0, Greater, 1], Element[{a, B}, Reals]]
gtt[r_] = (-r^2)*Exp[2*As[r]]*g[r]; 
g11[r_] = r^2*Exp[2*As[r]]*h[r]; 
grr[r_] = Exp[2*As[r]]/(r^2*g[r]); 
g[r_] = 1 - (Exp[(3*a - B^2)*(1/r^2)]*(3*(a/r^2) - B^2/r^2 - 1) + 1)/
     (Exp[(3*a - B^2)*(1/rh^2)]*(3*(a/rh^2) - B^2/rh^2 - 1) + 1); 
A[r_] = -(a/r^2); 
p[r_] = ((9*a - B^2)*Log[Sqrt[6*a^2 - B^4]*Sqrt[(6*a^2 - B^4)/r^2 + 9*a - B^2] + 
        6*(a^2/r) - B^4/r])/Sqrt[6*a^2 - B^4] + 
    (1/r)*Sqrt[(6*a^2 - B^4)/r^2 + 9*a - B^2] - 
    ((9*a - B^2)*Log[Sqrt[9*a - B^2]*Sqrt[6*a^2 - B^4]])/Sqrt[6*a^2 - B^4]; 
As[r_] = A[r] + Sqrt[1/6]*p[r]; 
h[r_] = 1; 

Answer 1

With no information about the metric tensor, the separation of variables yields

      Solve[dr/dl == Sqrt[g11[r]*gtt[r] - g11[r0]*gtt[r0]]/
                        Sqrt[grr[r]*gtt[r]*g11[r]], dl]

    dl -> (dr Sqrt[g11[r] grr[r] gtt[r]])/
               Sqrt[ g11[r] gtt[r] - g11[r0] gtt[r0]]

The integral cannot be solved, of course, symbolically

$$ l-l_0 = \int \frac{\sqrt{\text{g11}(r)\ \text{grr}(r) \ \text{gtt}(r)}}{\sqrt{\text{g11}(r)\ \text{gtt}(r)-\text{g11}(\text{r0}) \ \text{gtt}(\text{r0})}} \, dr$$

Insert functions and get the inverse

   InverseFunction[ Function[r,integral[r] ]][l-l_0]