2.902   ODE No. 902

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

$$y^{\prime }(x)=\frac{-3x^{4}y(x{)}^2+3x^{2}y(x{)}^4+x^6+x^3-xy(x{)}^2-y(x{)}^6-x}{y(x)(x^2-y(x{)}^2-1)}$$ ✓ Mathematica : cpu = 0.191283 (sec), leaf count = 295

$$\{\{y(x)\to -\frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}-\frac{\sqrt{-4x+1+4c_1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}-\frac{\sqrt{-4x+1+4c_1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to -\frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}+\frac{\sqrt{-4x+1+4c_1}}{x-c_1}-\frac{1}{x-c_1}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{4x^3}{x-c_1}-\frac{4c_1{x}^2}{x-c_1}+\frac{\sqrt{-4x+1+4c_1}}{x-c_1}-\frac{1}{x-c_1}}\}\}$$ ✓ Maple : cpu = 0.394 (sec), leaf count = 183

$$\{y\left(x\right)=\frac{1}{6x+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{(3x+\mathit{\_}\mathit{C}\mathit{1})(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3-\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)},y\left(x\right)=\frac{1}{6x+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{(3x+\mathit{\_}\mathit{C}\mathit{1})(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)},y\left(x\right)=-\frac{1}{6x+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{(3x+\mathit{\_}\mathit{C}\mathit{1})(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3-\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)},y\left(x\right)=-\frac{1}{6x+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{(3x+\mathit{\_}\mathit{C}\mathit{1})(4\mathit{\_}\mathit{C}\mathit{1}{x}^2+12x^3+\sqrt{-12\mathit{\_}\mathit{C}\mathit{1}-36x+9}-3)}\}$$