\[ y'(x)=\text {$\_$F1}(y(x)-\log (\sinh (x)))+\coth (x) \] ✓ Mathematica : cpu = 0.182105 (sec), leaf count = 157
\[\text {Solve}\left [\int _1^{y(x)}-\frac {\text {$\_$F1}(K[2]-\log (\sinh (x))) \int _1^x\left (\frac {(\coth (K[1])+\text {$\_$F1}(K[2]-\log (\sinh (K[1])))) \text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{(\text {$\_$F1}(K[2]-\log (\sinh (K[1])))){}^2}-\frac {\text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{\text {$\_$F1}(K[2]-\log (\sinh (K[1])))}\right )dK[1]-1}{\text {$\_$F1}(K[2]-\log (\sinh (x)))}dK[2]+\int _1^x-\frac {\coth (K[1])+\text {$\_$F1}(y(x)-\log (\sinh (K[1])))}{\text {$\_$F1}(y(x)-\log (\sinh (K[1])))}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.572 (sec), leaf count = 27
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\! \left ( {\it \_F1} \left ( {\it \_a}-\ln \left ( \sinh \left ( x \right ) \right ) \right ) \right ) ^{-1}\,{\rm d}{\it \_a}-x-{\it \_C1}=0 \right \} \]