3.898   ODE No. 898

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/16\frac{32x^{5}y\left(x\right)+8x^3+32x^5+64x^6{\left(y\left(x\right)\right)}^3+48x^4{\left(y\left(x\right)\right)}^2+12x^{2}y\left(x\right)+1}{x^6(4x^{2}y\left(x\right)+1+4x^2)}=0}}$$

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

Mathematica: cpu = 0.021503 (sec), leaf count = 106 $$\{\{y(x)\to \frac{1}{64x^8(\frac{1}{64x^8}-\frac{1}{x^8\sqrt{c_1+\frac{8192}{x}}})}-\frac{4x^2+1}{4x^2}\},\{y(x)\to \frac{1}{64x^8(\frac{1}{x^8\sqrt{c_1+\frac{8192}{x}}}+\frac{1}{64x^8})}-\frac{4x^2+1}{4x^2}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 83 $$\{y\left(x\right)=-\frac{1}{4x^2}(-4x^2+\sqrt{\frac{x\mathit{\_}\mathit{C}\mathit{1}+2}{x}}-1){(\sqrt{\frac{x\mathit{\_}\mathit{C}\mathit{1}+2}{x}}-1)}^{-1},y\left(x\right)=-\frac{1}{4x^2}(4x^2+\sqrt{\frac{x\mathit{\_}\mathit{C}\mathit{1}+2}{x}}+1){(\sqrt{\frac{x\mathit{\_}\mathit{C}\mathit{1}+2}{x}}+1)}^{-1}\}$$