2.325   ODE No. 325

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

$$\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})(\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}{)}^3-2{\text{Global}\stackrel{`}{}\text{x}}^3){\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})+\text{Global}\stackrel{`}{}\text{x}(2\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}{)}^3-{\text{Global}\stackrel{`}{}\text{x}}^3)=0$$ ✓ Mathematica : cpu = 0.0490209 (sec), leaf count = 139

$$\text{Solve}[\frac{1}{7}\text{RootSum}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}+1\mathrm{\&},\frac{8{\mathrm{\#}\text{1}}^3\log (\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}-\mathrm{\#}\text{1})+9{\mathrm{\#}\text{1}}^2\log (\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}-\mathrm{\#}\text{1})+12\mathrm{\#}\text{1}\log (\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}-\mathrm{\#}\text{1})-\log (\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}-\mathrm{\#}\text{1})}{4{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2+6\mathrm{\#}\text{1}+1}\mathrm{\&}]-\frac{1}{7}\log (1-\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}})=c_1-\log (\text{Global}\stackrel{`}{}\text{x}),\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})]$$

✓ Maple : cpu = 0.532 (sec), leaf count = 120

$$\{\frac{1}{7}\ln (-\frac{x-y\left(x\right)}{x})-\frac{2}{7}\ln \left(4\frac{x^4+x^{3}y\left(x\right)+3x^2{\left(y\left(x\right)\right)}^2+x{\left(y\left(x\right)\right)}^3+{\left(y\left(x\right)\right)}^4}{x^4}\right)+\frac{2\sqrt{3}}{7}\arctan \left(\frac{\sqrt{3}(x^3+4x^{2}y\left(x\right)+2x{\left(y\left(x\right)\right)}^2+2{\left(y\left(x\right)\right)}^3)}{3x^3}\right)-\frac{2\sqrt{3}}{7}\arctan \left(\frac{(x+2y\left(x\right))\sqrt{3}}{3x}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$