2.614   ODE No. 614

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

$$y^{\prime }(x)=\frac{(a-1)(a+1)x}{a^{2}F(-\frac{1}{2}{a}^2{x}^2+\frac{x^2}{2}+\frac{y(x{)}^2}{2})-F(-\frac{1}{2}{a}^2{x}^2+\frac{x^2}{2}+\frac{y(x{)}^2}{2})+y(x)}$$ ✓ Mathematica : cpu = 0.373455 (sec), leaf count = 177

$$\text{Solve}[{\int }_1^{y(x)}(\frac{K[2]}{(a-1)(a+1)F(-\frac{1}{2}{a}^2{x}^2+\frac{x^2}{2}+\frac{K[2{]}^2}{2})}-{\int }_1^x\frac{K[1]K[2]F^{\prime }(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{K[2{]}^2}{2})}{F{(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{K[2{]}^2}{2})}^2}dK[1]+1)dK[2]+{\int }_1^x-\frac{K[1]}{F(-\frac{1}{2}{a}^{2}K[1{]}^2+\frac{K[1{]}^2}{2}+\frac{y(x{)}^2}{2})}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.482 (sec), leaf count = 60

$$\{\frac{y\left(x\right)}{(a-1)(a+1)}+\frac{1}{2a^4-4a^2+2}{\int }^{-a^2{x}^2+x^2+{\left(y\left(x\right)\right)}^2}{\left(F\left(\frac{\mathit{\_}\mathit{a}}{2}\right)\right)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$