#### 2.714   ODE No. 714

$y'(x)=-\frac {y(x) \left (x^3 y(x)+x^2 y(x) \log (x)-x^2+e^x-x \log (x)-\log \left (\frac {1}{x}\right )\right )}{x \left (e^x-\log \left (\frac {1}{x}\right )\right )}$ Mathematica : cpu = 1.34968 (sec), leaf count = 162

$\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x-\frac {-K[1]^2-\log (K[1]) K[1]+e^{K[1]}-\log \left (\frac {1}{K[1]}\right )}{K[1] \left (e^{K[1]}-\log \left (\frac {1}{K[1]}\right )\right )}dK[1]\right )}{-\int _1^x-\frac {\exp \left (\int _1^{K[2]}-\frac {-K[1]^2-\log (K[1]) K[1]+e^{K[1]}-\log \left (\frac {1}{K[1]}\right )}{K[1] \left (e^{K[1]}-\log \left (\frac {1}{K[1]}\right )\right )}dK[1]\right ) \left (K[2]^3+\log (K[2]) K[2]^2\right )}{K[2] \left (e^{K[2]}-\log \left (\frac {1}{K[2]}\right )\right )}dK[2]+c_1}\right \}\right \}$ Maple : cpu = 0.362 (sec), leaf count = 96

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