3.404   ODE No. 404

$$\boxed{{\displaystyle a{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+b{x}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+cxy\left(x\right)=0}}$$

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.686 (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{ac\mathit{\_}\mathit{a}}{(-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{ac\mathit{\_}\mathit{a}}{(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\}$$