\[ y'(x)=\text {$\_$F1}(y(x)-\log (\sinh (x)))+\coth (x) \] ✓ Mathematica : cpu = 0.268143 (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 = 0.545 (sec), leaf count = 27
\[\left \{-c_{1}-x +\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{\textit {\_F1} \left (\textit {\_a} -\ln \left (\sinh \left (x \right )\right )\right )}d \textit {\_a} = 0\right \}\]