3.617   ODE No. 617

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/9\frac{x{\left(y\left(x\right)\right)}^2{\mathrm{e}}^{3x^2}}{{\mathrm{e}}^{9/2x^2}}F\left(1/3\frac{(3+y\left(x\right)){\mathrm{e}}^{3/2x^2}}{y\left(x\right)}\right)=0}}$$

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

Mathematica: cpu = 67.610585 (sec), leaf count = 612 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(-\frac{K[2](\frac{e^{\frac{3K[1{]}^2}{2}}}{3K[2]}-\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2{]}^2})K[1]F^{\prime }\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)}{K[2]F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)-9e^{\frac{3K[1{]}^2}{2}}K[2]-27e^{\frac{3K[1{]}^2}{2}}}+\frac{K[2]K[1]F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)(K[2](\frac{e^{\frac{3K[1{]}^2}{2}}}{3K[2]}-\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2{]}^2})F^{\prime }\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)+F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)-9e^{\frac{3K[1{]}^2}{2}})}{{(K[2]F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)-9e^{\frac{3K[1{]}^2}{2}}K[2]-27e^{\frac{3K[1{]}^2}{2}})}^2}-\frac{K[1]F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)}{K[2]F\left(\frac{e^{\frac{3K[1{]}^2}{2}}(K[2]+3)}{3K[2]}\right)-9e^{\frac{3K[1{]}^2}{2}}K[2]-27e^{\frac{3K[1{]}^2}{2}}})dK[1]+\frac{9e^{\frac{3x^2}{2}}-F\left(\frac{e^{\frac{3x^2}{2}}(K[2]+3)}{3K[2]}\right)}{3(K[2](9e^{\frac{3x^2}{2}}-F\left(\frac{e^{\frac{3x^2}{2}}(K[2]+3)}{3K[2]}\right))+27e^{\frac{3x^2}{2}})}-\frac{1}{3K[2]})dK[2]+{\int }_1^x-\frac{y(x)K[1]F\left(\frac{(y(x)+3)e^{\frac{3K[1{]}^2}{2}}}{3y(x)}\right)}{y(x)F\left(\frac{(y(x)+3)e^{\frac{3K[1{]}^2}{2}}}{3y(x)}\right)-9y(x)e^{\frac{3K[1{]}^2}{2}}-27e^{\frac{3K[1{]}^2}{2}}}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.234 (sec), leaf count = 47 $$\{y\left(x\right)=-3\frac{{\mathrm{e}}^{3/2x^2}}{{\mathrm{e}}^{3/2x^2}-3\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x^2-18{\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)-27\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})}\}$$