#### 2.791   ODE No. 791

$y'(x)=\frac {\text {sech}\left (\frac {1}{x-1}\right ) \left (x^5+x^4-2 x^3 y(x)-2 x^2 y(x)+2 x^2 \cosh \left (\frac {1}{x-1}\right )+x y(x)^2+y(x)^2-x-2 x \cosh \left (\frac {1}{x-1}\right )-1\right )}{x-1}$ Mathematica : cpu = 7.89596 (sec), leaf count = 110

$\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {2 (K[5]+1) \text {sech}\left (\frac {1}{K[5]-1}\right )}{K[5]-1}dK[5]\right )}{c_1-\int _1^x\frac {\exp \left (\int _1^{K[6]}\frac {2 (K[5]+1) \text {sech}\left (\frac {1}{K[5]-1}\right )}{K[5]-1}dK[5]\right ) (K[6]+1) \text {sech}\left (\frac {1}{K[6]-1}\right )}{K[6]-1}dK[6]}+\frac {x^3+x^2}{x+1}+1\right \}\right \}$ Maple : cpu = 13.26 (sec), leaf count = 306

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