#### 2.608   ODE No. 608

$y'(x)=\frac {\sqrt {y(x)}}{F\left (\frac {x-y(x)}{\sqrt {y(x)}}\right )+\sqrt {y(x)}}$ Mathematica : cpu = 0.409511 (sec), leaf count = 274

$\text {Solve}\left [\int _1^{y(x)}\left (-\frac {F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )}{x \sqrt {K[2]}}-\int _1^x-\frac {-\frac {F\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )}{\sqrt {K[2]}}-2 \left (-\frac {K[1]-K[2]}{2 K[2]^{3/2}}-\frac {1}{\sqrt {K[2]}}\right ) \sqrt {K[2]} F'\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )-1}{\left (-2 \sqrt {K[2]} F\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )+K[1]-K[2]\right )^2}dK[1]+\frac {2 F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )^2+\sqrt {K[2]} F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )+x}{x \left (-x+K[2]+2 F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right ) \sqrt {K[2]}\right )}\right )dK[2]+\int _1^x\frac {1}{-2 \sqrt {y(x)} F\left (\frac {K[1]-y(x)}{\sqrt {y(x)}}\right )+K[1]-y(x)}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.351 (sec), leaf count = 40

$\left \{ {\frac {\ln \left ( y \left ( x \right ) \right ) }{2}}-\int ^{{x{\frac {1}{\sqrt {y \left ( x \right ) }}}}-\sqrt {y \left ( x \right ) }}\! \left ( 2\,F \left ( {\it \_a} \right ) -{\it \_a} \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0 \right \}$