#### 2.803   ODE No. 803

$y'(x)=\frac {\text {\_F1}\left (y(x)^2-2 \log (x)\right )}{x \sqrt {y(x)^2}}$ Mathematica : cpu = 0.30093 (sec), leaf count = 637

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{\left (\text {\_F1}\left (K[2]^2-2 \log (x)\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (x)\right )+1\right )}-\int _1^x\left (\frac {2 K[2] \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ){}^2 \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 K[2] \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right ){}^2}-\frac {4 K[2] \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right ) \text {\_F1}\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 \sqrt {K[2]^2} \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right ) \text {\_F1}\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ){}^2 \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 \sqrt {K[2]^2} \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right ) \text {\_F1}\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right ){}^2}-\frac {2 \sqrt {K[2]^2} \text {\_F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}\right )dK[1]+\frac {\sqrt {K[2]^2} \text {\_F1}\left (K[2]^2-2 \log (x)\right )}{\left (\text {\_F1}\left (K[2]^2-2 \log (x)\right )-1\right ) \left (\text {\_F1}\left (K[2]^2-2 \log (x)\right )+1\right )}\right )dK[2]+\int _1^x\left (-\frac {\left (\text {\_F1}\left (y(x)^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\text {\_F1}\left (y(x)^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (y(x)^2-2 \log (K[1])\right )+1\right )}-\frac {\sqrt {y(x)^2} \text {\_F1}\left (y(x)^2-2 \log (K[1])\right )}{K[1] y(x) \left (\text {\_F1}\left (y(x)^2-2 \log (K[1])\right )-1\right ) \left (\text {\_F1}\left (y(x)^2-2 \log (K[1])\right )+1\right )}\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.994 (sec), leaf count = 65

$\left \{ y \left ( x \right ) =\sqrt {2\,\ln \left ( x \right ) +2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {2\,\ln \left ( x \right ) +2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) } \right \}$