3.536   ODE No. 536

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

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

Mathematica: cpu = 0.023503 (sec), leaf count = 86 $$\{\{y(x)\to c_1-\frac{b{x}^2}{2}\},\{y(x)\to c_1-{\tan }^{-1}\left(\frac{x\sqrt{a^2-x^2}}{x^2-a^2}\right)\},\{y(x)\to {\tan }^{-1}\left(\frac{x\sqrt{a^2-x^2}}{x^2-a^2}\right)+c_1\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 52 $$\{y\left(x\right)=-\frac{b{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=-\arctan \left(x\frac{1}{\sqrt{a^2-x^2}}\right)+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\arctan \left(x\frac{1}{\sqrt{a^2-x^2}}\right)+\mathit{\_}\mathit{C}\mathit{1}\}$$