2.404   ODE No. 404

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

$$a{y}^{\prime }(x{)}^2+b{x}^2{y}^{\prime }(x)+cxy(x)=0$$ ✗ Mathematica : cpu = 300.002 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 0.26 (sec), leaf count = 499

$$\{{\int }_{\mathit{\_}\mathit{b}}^x-1(-b{\mathit{\_}\mathit{a}}^2+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}acy\left(x\right)}){(-b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}acy\left(x\right)}\mathit{\_}\mathit{a}-6ay\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}2\frac{a}{-b{x}^3+\sqrt{b^2{x}^4-4\mathit{\_}\mathit{f}acx}x-6a\mathit{\_}\mathit{f}}-{\int }_{\mathit{\_}\mathit{b}}^{x}1(-b{\mathit{\_}\mathit{a}}^2+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac})(-2\frac{{\mathit{\_}\mathit{a}}^{2}ac}{\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}}-6a){(-b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}\mathit{\_}\mathit{a}-6a\mathit{\_}\mathit{f})}^{-2}+2\frac{\mathit{\_}\mathit{a}ac}{(-b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}\mathit{\_}\mathit{a}-6a\mathit{\_}\mathit{f})\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x-1(b{\mathit{\_}\mathit{a}}^2+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}acy\left(x\right)}){(b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}acy\left(x\right)}\mathit{\_}\mathit{a}+6ay\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-2\frac{a}{b{x}^3+\sqrt{b^2{x}^4-4\mathit{\_}\mathit{f}acx}x+6a\mathit{\_}\mathit{f}}-{\int }_{\mathit{\_}\mathit{b}}^{x}1(b{\mathit{\_}\mathit{a}}^2+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac})(-2\frac{{\mathit{\_}\mathit{a}}^{2}ac}{\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}}+6a){(b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}\mathit{\_}\mathit{a}+6a\mathit{\_}\mathit{f})}^{-2}+2\frac{\mathit{\_}\mathit{a}ac}{(b{\mathit{\_}\mathit{a}}^3+\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}\mathit{\_}\mathit{a}+6a\mathit{\_}\mathit{f})\sqrt{{\mathit{\_}\mathit{a}}^4{b}^2-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}ac}}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$