\[ y'(x)=\text {$\_$F1}(y(x)-\log (\sinh (x)))+\coth (x) \] ✓ Mathematica : cpu = 0.211298 (sec), leaf count = 157
DSolve[Derivative[1][y][x] == Coth[x] + _F1[-Log[Sinh[x]] + y[x]],y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {\text {$\_$F1}(K[2]-\log (\sinh (x))) \int _1^x\left (\frac {(\coth (K[1])+\text {$\_$F1}(K[2]-\log (\sinh (K[1])))) \text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{(\text {$\_$F1}(K[2]-\log (\sinh (K[1])))){}^2}-\frac {\text {$\_$F1}'(K[2]-\log (\sinh (K[1])))}{\text {$\_$F1}(K[2]-\log (\sinh (K[1])))}\right )dK[1]-1}{\text {$\_$F1}(K[2]-\log (\sinh (x)))}dK[2]+\int _1^x-\frac {\coth (K[1])+\text {$\_$F1}(y(x)-\log (\sinh (K[1])))}{\text {$\_$F1}(y(x)-\log (\sinh (K[1])))}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.595 (sec), leaf count = 27
dsolve(diff(y(x),x) = 1/sinh(x)*cosh(x)+_F1(y(x)-ln(sinh(x))),y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{\textit {\_F1} \left (\textit {\_a} -\ln \left (\sinh \left (x \right )\right )\right )}d \textit {\_a} -x -c_{1} = 0\]