\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {\cosh \left ( x \right ) }{\sinh \left ( x \right ) }}+{\it \_F1} \left ( y \left ( x \right ) -\ln \left ( \sinh \left ( x \right ) \right ) \right ) =0} \]
Mathematica: cpu = 0.109014 (sec), leaf count = 154 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {\text {$\_$F1}(K[2]-\log (\sinh (x))) \left (\int _1^x \left (\frac {\text {$\_$F1}'(K[2]-\log (\sinh (K[1]))) (\text {$\_$F1}(K[2]-\log (\sinh (K[1])))+\coth (K[1]))}{(\text {$\_$F1}(K[2]-\log (\sinh (K[1])))){}^2}-\frac {\text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{\text {$\_$F1}(K[2]-\log (\sinh (K[1])))}\right ) \, dK[1]\right )-1}{\text {$\_$F1}(K[2]-\log (\sinh (x)))} \, dK[2]+\int _1^x -\frac {\text {$\_$F1}(y(x)-\log (\sinh (K[1])))+\coth (K[1])}{\text {$\_$F1}(y(x)-\log (\sinh (K[1])))} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.405 (sec), leaf count = 27 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\! \left ( {\it \_F1} \left ( {\it \_a}-\ln \left ( \sinh \left ( x \right ) \right ) \right ) \right ) ^{-1}\,{\rm d}{\it \_a}-x-{\it \_C1}=0 \right \} \]