2.57   ODE No. 57

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

$$y^{\prime }(x)-\sqrt{|y(x)|}=0$$ ✓ Mathematica : cpu = 168.671 (sec), leaf count = 263

$$\left\{\{y(x)\to \text{InverseFunction}[-\frac{22^{3/4}(1-\mathrm{\#}\text{1})\sqrt[4]{1+\frac{i(1-\mathrm{\Re }(\mathrm{\#}\text{1}))}{|\mathrm{\Im }(\mathrm{\#}\text{1})|}}(i|\mathrm{\Im }(\mathrm{\#}\text{1})|-\mathrm{\Re }(\mathrm{\#}\text{1})+1){}_2{F}_1(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{i({\mathrm{\#}\text{1}}^{\ast }+\mathrm{\#}\text{1}-2)}{4|\mathrm{\Im }(\mathrm{\#}\text{1})|}+\frac{1}{2})}{3(\mathrm{\Im }(\mathrm{\#}\text{1}{)}^2+(1-\mathrm{\Re }(\mathrm{\#}\text{1}){)}^2)}-\frac{22^{3/4}(1-\mathrm{\#}\text{1})(-i|\mathrm{\Im }(\mathrm{\#}\text{1})|+\mathrm{\Im }(\mathrm{\#}\text{1}{)}^2+\mathrm{\Re }(\mathrm{\#}\text{1}{)}^2-\mathrm{\Re }(\mathrm{\#}\text{1}))\sqrt[4]{\frac{1+\frac{i((1-\mathrm{\Re }(\mathrm{\#}\text{1}))\mathrm{\Re }(\mathrm{\#}\text{1})-\mathrm{\Im }(\mathrm{\#}\text{1}{)}^2)}{|\mathrm{\Im }(\mathrm{\#}\text{1})|}}{\mathrm{\Im }(\mathrm{\#}\text{1}{)}^2+\mathrm{\Re }(\mathrm{\#}\text{1}{)}^2}}{}_2{F}_1(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{i(2{\left|\mathrm{\#}\text{1}\right|}^2-{\mathrm{\#}\text{1}}^{\ast }-\mathrm{\#}\text{1})}{4|\mathrm{\Im }(\mathrm{\#}\text{1})|}+\frac{1}{2})}{3(\mathrm{\Im }(\mathrm{\#}\text{1}{)}^2+(1-\mathrm{\Re }(\mathrm{\#}\text{1}){)}^2)}\mathrm{\&}][c_1+x]\}\right\}$$

✓ Maple : cpu = 0.138 (sec), leaf count = 31

$$\{x-\{\begin{array}{ll}-2\sqrt{-y\left(x\right)}& y\left(x\right)\le 0\\ 2\sqrt{y\left(x\right)}& 0<y\left(x\right)\end{array}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$