3.902   ODE No. 902

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{-x{\left(y\left(x\right)\right)}^2+x^3-x-{\left(y\left(x\right)\right)}^6+3x^2{\left(y\left(x\right)\right)}^4-3x^4{\left(y\left(x\right)\right)}^2+x^6}{(-{\left(y\left(x\right)\right)}^2+x^2-1)y\left(x\right)}=0}}$$

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

Mathematica: cpu = 0.109514 (sec), leaf count = 295 $$\{\{y(x)\to -\frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}-\frac{\sqrt{4c_1-4x+1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}-\frac{\sqrt{4c_1-4x+1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to -\frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}+\frac{\sqrt{4c_1-4x+1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}+\frac{\sqrt{4c_1-4x+1}}{x-c_1}-\frac{1}{x-c_1}}\}\}$$

Maple: cpu = 0.171 (sec), leaf count = 175 $$\{y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}+6x}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}+3x)(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)},y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}+6x}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}+3x)(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)},y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}+6x}\sqrt{-(\mathit{\_}\mathit{C}\mathit{1}+3x)(-4\mathit{\_}\mathit{C}\mathit{1}{x}^2-12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}+3)},y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}+6x}\sqrt{-(\mathit{\_}\mathit{C}\mathit{1}+3x)(-4\mathit{\_}\mathit{C}\mathit{1}{x}^2-12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}+3)}\}$$