3.813   ODE No. 813

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/2(-\sqrt{a}{x}^3+2\sqrt{a{x}^4+8y\left(x\right)}+2x^2\sqrt{a{x}^4+8y\left(x\right)}+2x^3\sqrt{a{x}^4+8y\left(x\right)})\sqrt{a}=0}}$$

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

Mathematica: cpu = 0.493063 (sec), leaf count = 66 $$\left\{\{y(x)\to \frac{1}{72}a(-72c_1{x}^4-96c_1{x}^3-288c_{1}x+144c_1^2+9x^8+24x^7+16x^6+72x^5+87x^4+144x^2)\}\right\}$$

Maple: cpu = 0.327 (sec), leaf count = 38 $$\{\frac{1}{4}\sqrt{a{x}^4+8y\left(x\right)}-\sqrt{a}(\frac{x^4}{4}+\frac{x^3}{3}+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$