2.1767   ODE No. 1767

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

$$(\frac{ax}{\sqrt{b^2-x^2}}-x)y^{\prime }(x{)}^2-y(x)y^{\prime }(x)+xy(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.245954 (sec), leaf count = 55

$$\left\{\{y(x)\to c_2\exp (\frac{\sqrt{b^2-x^2}}{a}+\frac{c_1\log (a\sqrt{b^2-x^2}-c_1)}{a^2})\}\right\}$$ ✓ Maple : cpu = 0.932 (sec), leaf count = 50

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\int -x\sqrt{b^2-x^2}{(\mathit{\_}\mathit{C}\mathit{1}\sqrt{b^2-x^2}+a(b^2-x^2))}^{-1}\mathrm{d}x}\}$$