8.177   ODE No. 1767

$$\boxed{{\displaystyle xy\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(\frac{ax}{\sqrt{b^2-x^2}}-x){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.075510 (sec), leaf count = 55 $$\left\{\{y(x)\to c_2\exp (\frac{c_1\log (a\sqrt{b^2-x^2}-c_1)}{a^2}+\frac{\sqrt{b^2-x^2}}{a})\}\right\}$$

Maple: cpu = 3.182 (sec), leaf count = 50 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\int -x\sqrt{b^2-x^2}{(a{b}^2-a{x}^2+\mathit{\_}\mathit{C}\mathit{1}\sqrt{b^2-x^2})}^{-1}\mathrm{d}x}\}$$