2.536   ODE No. 536

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

$$bx(x^2-a^2)y^{\prime }(x{)}^2+(x^2-a^2)y^{\prime }(x{)}^3+bx+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0250496 (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 = 0.041 (sec), leaf count = 52

$$\{y\left(x\right)=-\frac{b{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=-\arctan \left(x\frac{1}{\sqrt{a^2-x^2}}\right)+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\arctan \left(x\frac{1}{\sqrt{a^2-x^2}}\right)+\mathit{\_}\mathit{C}\mathit{1}\}$$