3.619   ODE No. 619

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=6\frac{y\left(x\right)}{8{\left(y\left(x\right)\right)}^4+9{\left(y\left(x\right)\right)}^3+12{\left(y\left(x\right)\right)}^2+6y\left(x\right)-F(-1/3{\left(y\left(x\right)\right)}^4-1/2{\left(y\left(x\right)\right)}^3-{\left(y\left(x\right)\right)}^2-y\left(x\right)+x)}=0}}$$

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

Mathematica: cpu = 60.581193 (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 = 0.359 (sec), leaf count = 81 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{\mathit{\_}\mathit{a}}(-8{\mathit{\_}\mathit{a}}^4-9{\mathit{\_}\mathit{a}}^3-12{\mathit{\_}\mathit{a}}^2+F(-\frac{{\mathit{\_}\mathit{a}}^4}{3}-\frac{{\mathit{\_}\mathit{a}}^3}{2}-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}+x)-6\mathit{\_}\mathit{a}){\left(F(-\frac{{\mathit{\_}\mathit{a}}^4}{3}-\frac{{\mathit{\_}\mathit{a}}^3}{2}-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}+x)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$