Getting infinite loop DE soln of the Schwarzschild metric in General Relativity geodesics equation

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The system of DE

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arises when using the Schwarzschild metric of General Relativity on the geodesics equation. I was trying to solve these equations for ##\phi## as a function of ##r##. I followed Weinberg (Weinberg's book S&G relativity) who uses ##t' = 1 / B(r)## in his book. So now we have two equations and two unkowns. I tried to solve it for ##\phi (r)## as I said above but Mathematica keeps running indefinitely and gives no solution. I was hoping to get the same result as Weinberg does in his book. What am I doing wrong?
 

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