2.590   ODE No. 590

\[ y'(x)=\frac {x}{F\left (x^2+y(x)^2\right )-y(x)} \] Mathematica : cpu = 0.2465 (sec), leaf count = 94


\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F\left (x^2+K[2]^2\right )}-\int _1^x\frac {2 K[1] K[2] F'\left (K[1]^2+K[2]^2\right )}{F\left (K[1]^2+K[2]^2\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{F\left (K[1]^2+y(x)^2\right )}dK[1]=c_1,y(x)\right ]\] Maple : cpu = 0.144 (sec), leaf count = 28


\[-y \relax (x )+\frac {\left (\int _{}^{y \relax (x )^{2}+x^{2}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}{2}-c_{1} = 0\]