3.609   ODE No. 609

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

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

Mathematica: cpu = 51.408028 (sec), leaf count = 114 $$\text{Solve}[{\int }_1^{y(x)}-\frac{F(x^{3}K[2]){\int }_1^x(\frac{3K[1{]}^{5}K[2]F^{\prime }(K[1{]}^{3}K[2])}{F{(K[1{]}^{3}K[2])}^2}-\frac{3K[1{]}^2}{F(K[1{]}^{3}K[2])})dK[1]+x^3}{F(x^{3}K[2])}dK[2]+{\int }_1^x(1-\frac{3y(x)K[1{]}^2}{F(y(x)K[1{]}^3)})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.140 (sec), leaf count = 22 $$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x-{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}{x^3}\}$$