#### 2.861   ODE No. 861

$y'(x)=-\frac {e^{-1/x} \left (-\text {\_F1}\left (e^{\frac {1}{x}} y(x)\right )-\frac {e^{\frac {1}{x}} y(x)}{x}\right )}{x}$ Mathematica : cpu = 1.45601 (sec), leaf count = 158

$\text {Solve}\left [\int _1^{y(x)}-\frac {\text {\_F1}\left (e^{\frac {1}{x}} K[2]\right ) \int _1^x\left (\frac {e^{\frac {1}{K[1]}}}{K[1]^2 \text {\_F1}\left (e^{\frac {1}{K[1]}} K[2]\right )}-\frac {e^{\frac {2}{K[1]}} K[2] \text {\_F1}'\left (e^{\frac {1}{K[1]}} K[2]\right )}{K[1]^2 \left (\text {\_F1}\left (e^{\frac {1}{K[1]}} K[2]\right )\right ){}^2}\right )dK[1]+e^{\frac {1}{x}}}{\text {\_F1}\left (e^{\frac {1}{x}} K[2]\right )}dK[2]+\int _1^x\left (\frac {e^{\frac {1}{K[1]}} y(x)}{K[1]^2 \text {\_F1}\left (e^{\frac {1}{K[1]}} y(x)\right )}+\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.274 (sec), leaf count = 26

$\left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{{\rm e}^{{x}^{-1}}}}} \right \}$