#### 2.594   ODE No. 594

$y'(x)=\frac {x F\left (\frac {y(x)^2-b}{x^2}\right )}{y(x)}$ Mathematica : cpu = 0.339759 (sec), leaf count = 236

$\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{-F\left (\frac {K[2]^2-b}{x^2}\right ) x^2+K[2]^2-b}-\int _1^x\left (\frac {F\left (\frac {K[2]^2-b}{K[1]^2}\right ) K[1] \left (2 K[2] F'\left (\frac {K[2]^2-b}{K[1]^2}\right )-2 K[2]\right )}{\left (F\left (\frac {K[2]^2-b}{K[1]^2}\right ) K[1]^2-K[2]^2+b\right )^2}-\frac {2 K[2] F'\left (\frac {K[2]^2-b}{K[1]^2}\right )}{K[1] \left (F\left (\frac {K[2]^2-b}{K[1]^2}\right ) K[1]^2-K[2]^2+b\right )}\right )dK[1]\right )dK[2]+\int _1^x-\frac {F\left (\frac {y(x)^2-b}{K[1]^2}\right ) K[1]}{F\left (\frac {y(x)^2-b}{K[1]^2}\right ) K[1]^2-y(x)^2+b}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.099 (sec), leaf count = 67

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