3.502   ODE No. 502

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

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

Mathematica: cpu = 1.717718 (sec), leaf count = 100 $$\{\{y(x)\to \frac{b{c}_1}{a}-\frac{\sqrt{2b^2{c}_{1}x-b^2{c}_1^2+b^2(-x^2)+c^2}}{a}\},\{y(x)\to \frac{\sqrt{2b^2{c}_{1}x-b^2{c}_1^2+b^2(-x^2)+c^2}}{a}+\frac{b{c}_1}{a}\}\}$$

Maple: cpu = 0.890 (sec), leaf count = 195 $$\{y\left(x\right)=\frac{bx-\sqrt{2}c}{a},y\left(x\right)=\frac{bx+\sqrt{2}c}{a},y\left(x\right)=\frac{1}{a}(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}\frac{a}{(2{\mathit{\_}\mathit{a}}^2{a}^2-4c^2)b}(-{\mathit{\_}\mathit{a}}^2{a}^2+2c^2+\sqrt{-a^2{\mathit{\_}\mathit{a}}^2({\mathit{\_}\mathit{a}}^2{a}^2-2c^2)})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})a+bx),y\left(x\right)=\frac{1}{a}(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}-\frac{a}{(2{\mathit{\_}\mathit{a}}^2{a}^2-4c^2)b}({\mathit{\_}\mathit{a}}^2{a}^2-2c^2+\sqrt{-a^2{\mathit{\_}\mathit{a}}^2({\mathit{\_}\mathit{a}}^2{a}^2-2c^2)})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})a+bx)\}$$