2.848   ODE No. 848

\[ y'(x)=\text {$\_$F1}(y(x)-\log (\sinh (x)))+\coth (x) \] Mathematica : cpu = 0.211298 (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 = 0.595 (sec), leaf count = 27


\[\int _{\textit {\_b}}^{y \relax (x )}\frac {1}{\textit {\_F1} \left (\textit {\_a} -\ln \left (\sinh \relax (x )\right )\right )}d \textit {\_a} -x -c_{1} = 0\]