3.895   ODE No. 895

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{(-256a{x}^{2}y\left(x\right)-32a^2{x}^6-256a{x}^2+512{\left(y\left(x\right)\right)}^3+192x^{4}a{\left(y\left(x\right)\right)}^2+24y\left(x\right)a^2{x}^8+a^3{x}^{12})x}{512y\left(x\right)+64a{x}^4+512}=0}}$$

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

Mathematica: cpu = 0.022503 (sec), leaf count = 81 $$\{\{y(x)\to \frac{1}{8}(-a{x}^4-8)[phone]\frac{\mathrm{}}{\mathrm{}\frac{\mathrm{}}{\mathrm{}}-\frac{1}{\sqrt{c_1-262144x^2}})}\},\{y(x)\to \frac{1}{8}(-a{x}^4-8)+\frac{1}{512(\frac{1}{\sqrt{c_1-262144x^2}}+\frac{1}{512})}\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 80 $$\{y\left(x\right)=-\frac{1}{8}(\sqrt{-x^2+\mathit{\_}\mathit{C}\mathit{1}}a{x}^4-a{x}^4-8){(-1+\sqrt{-x^2+\mathit{\_}\mathit{C}\mathit{1}})}^{-1},y\left(x\right)=-\frac{1}{8}(\sqrt{-x^2+\mathit{\_}\mathit{C}\mathit{1}}a{x}^4+a{x}^4+8){(1+\sqrt{-x^2+\mathit{\_}\mathit{C}\mathit{1}})}^{-1}\}$$