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 = 270.489 (sec), leaf count = 195

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

✓ Maple : cpu = 0.535 (sec), leaf count = 81

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