2.612   ODE No. 612

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

$$y^{\prime }(x)=\frac{1}{2}{e}^{\frac{x^2}{4}}(2F(e^{-\frac{x^2}{4}}y(x))+e^{-\frac{x^2}{4}}xy(x))$$ ✓ Mathematica : cpu = 0.355309 (sec), leaf count = 199

$$\text{Solve}[{\int }_1^{y(x)}-\frac{e^{-\frac{x^2}{4}}(e^{\frac{x^2}{4}}F(e^{-\frac{x^2}{4}}K[2]){\int }_1^x(\frac{e^{-\frac{1}{4}K[1{]}^2}K[1]}{2F(e^{-\frac{1}{4}K[1{]}^2}K[2])}-\frac{e^{-\frac{1}{2}K[1{]}^2}K[1]K[2]F^{\prime }(e^{-\frac{1}{4}K[1{]}^2}K[2])}{2F{(e^{-\frac{1}{4}K[1{]}^2}K[2])}^2})dK[1]+1)}{F(e^{-\frac{x^2}{4}}K[2])}dK[2]+{\int }_1^x(\frac{e^{-\frac{1}{4}K[1{]}^2}K[1]y(x)}{2F(e^{-\frac{1}{4}K[1{]}^2}y(x))}+1)dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.207 (sec), leaf count = 27

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