3.310   ODE No. 310

$$\boxed{{\displaystyle (2{\left(y\left(x\right)\right)}^3+5x^{2}y\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+5x{\left(y\left(x\right)\right)}^2+x^3=0}}$$

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

Mathematica: cpu = 0.044006 (sec), leaf count = 159 $$\{\{y(x)\to -\frac{\sqrt{-\sqrt{2e^{4c_1}+23x^4}-5x^2}}{\sqrt{2}}\},\{y(x)\to \frac{\sqrt{-\sqrt{2e^{4c_1}+23x^4}-5x^2}}{\sqrt{2}}\},\{y(x)\to -\frac{\sqrt{\sqrt{2e^{4c_1}+23x^4}-5x^2}}{\sqrt{2}}\},\{y(x)\to \frac{\sqrt{\sqrt{2e^{4c_1}+23x^4}-5x^2}}{\sqrt{2}}\}\}$$

Maple: cpu = 0.109 (sec), leaf count = 125 $$\{y\left(x\right)=-\frac{1}{2}\sqrt{-10x^2\mathit{\_}\mathit{C}\mathit{1}-2\sqrt{23x^4{\mathit{\_}\mathit{C}\mathit{1}}^2+2}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{1}{2}\sqrt{-10x^2\mathit{\_}\mathit{C}\mathit{1}-2\sqrt{23x^4{\mathit{\_}\mathit{C}\mathit{1}}^2+2}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=-\frac{1}{2}\sqrt{-10x^2\mathit{\_}\mathit{C}\mathit{1}+2\sqrt{23x^4{\mathit{\_}\mathit{C}\mathit{1}}^2+2}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{1}{2}\sqrt{-10x^2\mathit{\_}\mathit{C}\mathit{1}+2\sqrt{23x^4{\mathit{\_}\mathit{C}\mathit{1}}^2+2}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}}\}$$