3.594   ODE No. 594

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{x}{y\left(x\right)}F(-\frac{-{\left(y\left(x\right)\right)}^2+b}{x^2})=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 17.877770 (sec), leaf count = 233 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(\frac{K[1]F\left(\frac{K[2{]}^2-b}{K[1{]}^2}\right)(2K[2]F^{\prime }\left(\frac{K[2{]}^2-b}{K[1{]}^2}\right)-2K[2])}{{(K[1{]}^{2}F\left(\frac{K[2{]}^2-b}{K[1{]}^2}\right)-K[2{]}^2+b)}^2}-\frac{2K[2]F^{\prime }\left(\frac{K[2{]}^2-b}{K[1{]}^2}\right)}{K[1](K[1{]}^{2}F\left(\frac{K[2{]}^2-b}{K[1{]}^2}\right)-K[2{]}^2+b)})dK[1]-\frac{K[2]}{x^2(-F\left(\frac{K[2{]}^2-b}{x^2}\right))+K[2{]}^2-b})dK[2]+{\int }_1^x-\frac{K[1]F\left(\frac{y(x{)}^2-b}{K[1{]}^2}\right)}{K[1{]}^{2}F\left(\frac{y(x{)}^2-b}{K[1{]}^2}\right)+b-y(x{)}^2}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.140 (sec), leaf count = 67 $$\{y\left(x\right)=\sqrt{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})x^2+b},y\left(x\right)=-\sqrt{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})x^2+b}\}$$