2.619   ODE No. 619

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

$$y^{\prime }(x)=\frac{6y(x)}{-F(-\frac{1}{3}y(x{)}^4-\frac{y(x{)}^3}{2}-y(x{)}^2-y(x)+x)+8y(x{)}^4+9y(x{)}^3+12y(x{)}^2+6y(x)}$$ ✓ Mathematica : cpu = 248.478 (sec), leaf count = 327

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{F(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+x){\int }_1^x-\frac{6(-\frac{4}{3}K[2{]}^3-\frac{3K[2{]}^2}{2}-2K[2]-1)F^{\prime }(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+K[1])}{F{(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+K[1])}^2}dK[1]+6}{F(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+x)}-\frac{8K[2{]}^3}{F(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+x)}-\frac{9K[2{]}^2}{F(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+x)}-\frac{12K[2]}{F(-\frac{1}{3}K[2{]}^4-\frac{K[2{]}^3}{2}-K[2{]}^2-K[2]+x)}+\frac{1}{K[2]})dK[2]+{\int }_1^x\frac{6}{F(K[1]-\frac{1}{3}y(x{)}^4-\frac{y(x{)}^3}{2}-y(x{)}^2-y(x))}dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.487 (sec), leaf count = 81

$$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{\mathit{\_}\mathit{a}}(-8{\mathit{\_}\mathit{a}}^4-9{\mathit{\_}\mathit{a}}^3-12{\mathit{\_}\mathit{a}}^2+F(-\frac{{\mathit{\_}\mathit{a}}^4}{3}-\frac{{\mathit{\_}\mathit{a}}^3}{2}-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}+x)-6\mathit{\_}\mathit{a}){\left(F(-\frac{{\mathit{\_}\mathit{a}}^4}{3}-\frac{{\mathit{\_}\mathit{a}}^3}{2}-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}+x)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$