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 = 0.0157011 (sec), leaf count = 64

$$\{\{y(x)\to -\frac{b{x}^2}{2}+c_1\},\{y(x)\to -{\tan }^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)+c_1\},\{y(x)\to {\tan }^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)+c_1\}\}$$ ✓ Maple : cpu = 0.04 (sec), leaf count = 52

$$\{y\left(x\right)=c_1-\arctan \left(\frac{x}{\sqrt{a^2-x^2}}\right),y\left(x\right)=c_1+\arctan \left(\frac{x}{\sqrt{a^2-x^2}}\right),y\left(x\right)=-\frac{b{x}^2}{2}+c_1\}$$