\[ y'(x)=\text {$\_$F1}(y(x)-\log (\sinh (x)))+\coth (x) \] ✓ Mathematica : cpu = 0.124532 (sec), leaf count = 91
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {1}{\text {$\_$F1}(K[2]-\log (\sinh (x)))}-\int _1^x \frac {\coth (K[1]) \text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{(\text {$\_$F1}(K[2]-\log (\sinh (K[1])))){}^2} \, dK[1]\right ) \, dK[2]+\int _1^x \left (-\frac {\coth (K[1])}{\text {$\_$F1}(y(x)-\log (\sinh (K[1])))}-1\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.741 (sec), leaf count = 27
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\! \left ( {\it \_F1} \left ( {\it \_a}-\ln \left ( \sinh \left ( x \right ) \right ) \right ) \right ) ^{-1}\,{\rm d}{\it \_a}-x-{\it \_C1}=0 \right \} \]