2.583   ODE No. 583

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

$$y^{\prime }(x)=-\frac{1}{2}x(a{x}^2-2F(\frac{a{x}^4}{8}+y(x)))$$ ✓ Mathematica : cpu = 0.217244 (sec), leaf count = 126

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F(\frac{a{x}^4}{8}+K[2]){\int }_1^x\frac{aK[1{]}^3{F}^{\prime }(\frac{1}{8}aK[1{]}^4+K[2])}{2F{(\frac{1}{8}aK[1{]}^4+K[2])}^2}dK[1]+1}{F(\frac{a{x}^4}{8}+K[2])}dK[2]+{\int }_1^x(K[1]-\frac{aK[1{]}^3}{2F(\frac{1}{8}aK[1{]}^4+y(x))})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.209 (sec), leaf count = 31

$$\{y\left(x\right)=-\frac{a{x}^4}{8}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x^2+2{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})\}$$