#### 2.846   ODE No. 846

$y'(x)=\frac {1}{x^2 \left (-\left (\frac {1}{y(x)}+1\right )\right ) \text {\_F1}\left (x \left (\frac {1}{y(x)}+1\right )\right )+x^2 \text {\_F1}\left (x \left (\frac {1}{y(x)}+1\right )\right )+x \left (\frac {1}{y(x)}+1\right )-x}$ Mathematica : cpu = 0.892233 (sec), leaf count = 365

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {x \text {\_F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )-1}{x \text {\_F1}\left (x \left (1+\frac {1}{K[2]}\right )\right ) K[2]-K[2]+x \text {\_F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )}-\int _1^x\left (\frac {\text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {\_F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {\_F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}}{K[1] \left (K[2] \text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]}-\frac {\left (K[2] \text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right ) \left (K[1] \left (\text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {\_F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {\_F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}\right )-1\right )}{\left (K[1] \left (K[2] \text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {\_F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]\right ){}^2}\right )dK[1]\right )dK[2]+\int _1^x\left (\frac {y(x) \text {\_F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {\_F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )}{K[1] \left (y(x) \text {\_F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {\_F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )\right )-y(x)}-\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.144 (sec), leaf count = 40

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