2.325   ODE No. 325

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

$$y(x)(y(x{)}^3-2x^3)y^{\prime }(x)+x(2y(x{)}^3-x^3)=0$$ ✓ Mathematica : cpu = 0.186556 (sec), leaf count = 139

$$\text{Solve}[\frac{1}{7}\text{RootSum}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}+1\mathrm{\&},\frac{8{\mathrm{\#}\text{1}}^3\log (\frac{y(x)}{x}-\mathrm{\#}\text{1})+9{\mathrm{\#}\text{1}}^2\log (\frac{y(x)}{x}-\mathrm{\#}\text{1})+12\mathrm{\#}\text{1}\log (\frac{y(x)}{x}-\mathrm{\#}\text{1})-\log (\frac{y(x)}{x}-\mathrm{\#}\text{1})}{4{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2+6\mathrm{\#}\text{1}+1}\mathrm{\&}]-\frac{1}{7}\log (1-\frac{y(x)}{x})=-\log (x)+c_1,y(x)]$$ ✓ Maple : cpu = 0.541 (sec), leaf count = 124

$$\{\frac{1}{7}\ln \left(\frac{y\left(x\right)-x}{x}\right)-\frac{2}{7}\ln \left(\frac{4x^4+4x^{3}y\left(x\right)+12x^2{\left(y\left(x\right)\right)}^2+4x{\left(y\left(x\right)\right)}^3+4{\left(y\left(x\right)\right)}^4}{x^4}\right)-\frac{2\sqrt{3}}{7}\arctan \left(\frac{(x+2y\left(x\right))\sqrt{3}}{3x}\right)+\frac{2\sqrt{3}}{7}\arctan \left(\frac{\sqrt{3}(x^3+4x^{2}y\left(x\right)+2x{\left(y\left(x\right)\right)}^2+2{\left(y\left(x\right)\right)}^3)}{3x^3}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$