2.650   ODE No. 650

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

$$y^{\prime }(x)=x\sqrt{a^2+2ax+x^2+4y(x)}-\frac{a}{2}-\frac{x}{2}$$ ✓ Mathematica : cpu = 0.383047 (sec), leaf count = 109

$$\text{Solve}[-\frac{1}{2}\sqrt{a^2+2ax+x^2+4y(x)}-\frac{1}{2}a\log (\sqrt{a^2+2ax+x^2+4y(x)}+a+x)+\frac{1}{2}a{\tanh }^{-1}\left(\frac{2a+2x}{2\sqrt{a^2+2ax+x^2+4y(x)}}\right)+\frac{1}{4}a\log (y(x))+\frac{x^2}{2}=c_1,y(x)]$$ ✓ Maple : cpu = 0.491 (sec), leaf count = 28

$$\{\mathit{\_}\mathit{C}\mathit{1}+x^2+\frac{1}{2}-\sqrt{x^2+2ax+a^2+4y\left(x\right)}=0\}$$