3.583   ODE No. 583

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

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

Mathematica: cpu = 41.455764 (sec), leaf count = 123 $$\text{Solve}[{\int }_1^{y(x)}-\frac{F(K[2]+\frac{a{x}^4}{8}){\int }_1^x\frac{aK[1{]}^3{F}^{\prime }(\frac{1}{8}aK[1{]}^4+K[2])}{2F{(\frac{1}{8}aK[1{]}^4+K[2])}^2}dK[1]+1}{F(K[2]+\frac{a{x}^4}{8})}dK[2]+{\int }_1^x(K[1]-\frac{aK[1{]}^3}{2F(\frac{1}{8}aK[1{]}^4+y(x))})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.125 (sec), leaf count = 31 $$\{y\left(x\right)=-\frac{a{x}^4}{8}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x^2+2{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})\}$$