How to solve system of Differential Equations with 1 independent and 3 dependent variables

Question

How can one solve this set of three differential equations in one independent variable "t" and three dependent variables A, B and F, which are functions of only t? $$ \frac{F(t) B''(t)+B'(t) F'(t)+B(t) F''(t)}{B(t) F(t)}=0, \\ \frac{F(t) A''(t)+A'(t) F'(t)+A(t) F''(t)}{A(t) F(t)}=0, \\ \frac{A'(t)}{A(t)}+\frac{B'(t)}{B(t)}=0 $$ By the way, what are such systems called? I came across this set as Einstein's Equations for a certain space-time in General Relativity.

Answer 1

$$from-3rd-equation\\\frac{A'}{A}+\frac{B'}{B}=0\\\frac{A'B+AB'}{AB}=0\\(AB)'=0 \\AB=constant \\AB=c\\Put\\B=\frac{c}{A}\\B'=\frac{-cA'}{A^2}\\B''=\frac{-cA''A^2 +2AA'cA'}{A^4}=\frac{-c(A''A +2A'A')}{A^3}\\now\\put \\in- 1st-equation\\then- you - have -two-equation- with- A ,F $$