3.614   ODE No. 614

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

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

Mathematica: cpu = 72.937762 (sec), leaf count = 171 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x\frac{K[1]K[2]F^{\prime }(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{K[2{]}^2}{2})}{F{(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{K[2{]}^2}{2})}^2}dK[1]+\frac{K[2]}{(a^2-1)F(\frac{K[2{]}^2}{2}-\frac{1}{2}{a}^2{x}^2+\frac{x^2}{2})}+1)dK[2]+{\int }_1^x-\frac{K[1]}{F(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{y(x{)}^2}{2})}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.328 (sec), leaf count = 59 $$\{\frac{y\left(x\right)}{(a-1)(a+1)}+\frac{1}{2a^4-4a^2+2}{\int }^{-a^2{x}^2+x^2+{\left(y\left(x\right)\right)}^2}{\left(F\left(\frac{\mathit{\_}\mathit{a}}{2}\right)\right)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$