2.608   ODE No. 608

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

$$y^{\prime }(x)=\frac{\sqrt{y(x)}}{F\left(\frac{x-y(x)}{\sqrt{y(x)}}\right)+\sqrt{y(x)}}$$ ✓ Mathematica : cpu = 298.623 (sec), leaf count = 271

$$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x-\frac{-2(-\frac{K[1]-K[2]}{2K[2{]}^{3/2}}-\frac{1}{\sqrt{K[2]}})\sqrt{K[2]}{F}^{\prime }\left(\frac{K[1]-K[2]}{\sqrt{K[2]}}\right)-\frac{F\left(\frac{K[1]-K[2]}{\sqrt{K[2]}}\right)}{\sqrt{K[2]}}-1}{{(-2\sqrt{K[2]}F\left(\frac{K[1]-K[2]}{\sqrt{K[2]}}\right)+K[1]-K[2])}^2}dK[1]-\frac{F\left(\frac{x-K[2]}{\sqrt{K[2]}}\right)}{x\sqrt{K[2]}}+\frac{2F{\left(\frac{x-K[2]}{\sqrt{K[2]}}\right)}^2+\sqrt{K[2]}F\left(\frac{x-K[2]}{\sqrt{K[2]}}\right)+x}{x(2\sqrt{K[2]}F\left(\frac{x-K[2]}{\sqrt{K[2]}}\right)+K[2]-x)})dK[2]+{\int }_1^x\frac{1}{-2\sqrt{y(x)}F\left(\frac{K[1]-y(x)}{\sqrt{y(x)}}\right)+K[1]-y(x)}dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.153 (sec), leaf count = 40

$$\{\frac{\ln \left(y\left(x\right)\right)}{2}-{\int }^{x\frac{1}{\sqrt{y\left(x\right)}}-\sqrt{y\left(x\right)}}{(2F\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$