#### 2.797   ODE No. 797

$y'(x)=\frac {y(x) \left (x^3 y(x) \cosh \left (\frac {x+1}{x-1}\right )+x^2 y(x) \cosh \left (\frac {x+1}{x-1}\right )-x^2 \cosh \left (\frac {x+1}{x-1}\right )-x \cosh \left (\frac {x+1}{x-1}\right )-1\right )}{x}$ Mathematica : cpu = 1.90146 (sec), leaf count = 349

$\left \{\left \{y(x)\to \frac {\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}-\frac {1}{4} e x^2 \sinh \left (\frac {2}{x-1}\right )+\frac {x^2 \sinh \left (\frac {2}{x-1}\right )}{4 e}-\frac {1}{4} e x^2 \cosh \left (\frac {2}{x-1}\right )-\frac {x^2 \cosh \left (\frac {2}{x-1}\right )}{4 e}-e x \sinh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \sinh \left (\frac {2}{x-1}\right )-\frac {\sinh \left (\frac {2}{x-1}\right )}{4 e}-e x \cosh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \cosh \left (\frac {2}{x-1}\right )+\frac {\cosh \left (\frac {2}{x-1}\right )}{4 e}+\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )}{x \left (\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}\right )+c_1 \exp \left (\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )\right )}\right \}\right \}$ Maple : cpu = 0.258 (sec), leaf count = 168

$\left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {{\rm e}^{{\frac {{x}^{2}-1}{4}{{\rm e}^{{\frac {-1-x}{x-1}}}}}+{\frac {{x}^{2}+4\,x-5}{4}{{\rm e}^{{\frac {1+x}{x-1}}}}}-{\it Ei} \left ( 1,2\, \left ( x-1 \right ) ^{-1} \right ) {{\rm e}^{-1}}+3\,{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) {\rm e}}} \right ) ^{-1} \left ( {\it \_C1}+\int \!-\cosh \left ( {\frac {1+x}{x-1}} \right ) {{\rm e}^{{\frac {-{x}^{2}+1}{4}{{\rm e}^{{\frac {-1-x}{x-1}}}}}+{\frac {-{x}^{2}-4\,x+5}{4}{{\rm e}^{{\frac {1+x}{x-1}}}}}+{\it Ei} \left ( 1,2\, \left ( x-1 \right ) ^{-1} \right ) {{\rm e}^{-1}}-3\,{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) {\rm e}}} \left ( 1+x \right ) \,{\rm d}x \right ) ^{-1}} \right \}$