3.454   ODE No. 454

$$\boxed{{\displaystyle a{x}^2{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2axy\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^2-a(a-1)x^2=0}}$$

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

Mathematica: cpu = 0.154520 (sec), leaf count = 118 $$\{\{y(x)\to \frac{1}{2}{e}^{-c_1}{x}^{1-\frac{\sqrt{a-1}}{\sqrt{a}}}(e^{2c_1}-a{x}^{\frac{2\sqrt{a-1}}{\sqrt{a}}})\},\{y(x)\to \frac{1}{2}{e}^{-c_1}{x}^{1-\frac{\sqrt{a-1}}{\sqrt{a}}}(e^{2c_1}{x}^{\frac{2\sqrt{a-1}}{\sqrt{a}}}-a)\}\}$$

Maple: cpu = 0.593 (sec), leaf count = 138 $$\{y\left(x\right)=\sqrt{-a}x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{a}}^{2}a-{\mathit{\_}\mathit{a}}^2+a^2-a}\sqrt{({\mathit{\_}\mathit{a}}^{2}a-{\mathit{\_}\mathit{a}}^2+a^2-a)a}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{a}}^{2}a-{\mathit{\_}\mathit{a}}^2+a^2-a}\sqrt{({\mathit{\_}\mathit{a}}^{2}a-{\mathit{\_}\mathit{a}}^2+a^2-a)a}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=-\sqrt{-a}x\}$$