#### 2.614   ODE No. 614

$y'(x)=\frac {(a-1) (a+1) x}{a^2 F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {y(x)^2}{2}\right )-F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {y(x)^2}{2}\right )+y(x)}$ Mathematica : cpu = 0.358399 (sec), leaf count = 177

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{(a-1) (a+1) F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {K[2]^2}{2}\right )}-\int _1^x\frac {K[1] K[2] F'\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {K[2]^2}{2}\right )}{F\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {K[2]^2}{2}\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{F\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {y(x)^2}{2}\right )}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.332 (sec), leaf count = 60

$\left \{ {\frac {y \left ( x \right ) }{ \left ( a-1 \right ) \left ( a+1 \right ) }}+{\frac {1}{2\,{a}^{4}-4\,{a}^{2}+2}\int ^{-{a}^{2}{x}^{2}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}}\! \left ( F \left ( {\frac {{\it \_a}}{2}} \right ) \right ) ^{-1}{d{\it \_a}}}-{\it \_C1}=0 \right \}$