ODE No. 626

$$y^{\prime }(x)=\frac{x}{\sqrt{x^2+1}+y(x)}$$ ✓ Mathematica : cpu = 0.212384 (sec), leaf count = 88

DSolve[Derivative[1][y][x] == x/(Sqrt[1 + x^2] + y[x]),y[x],x]
 

$$\text{Solve}[\frac{1}{2}(\log (-\frac{y(x{)}^2}{x^2+1}-\frac{y(x)}{\sqrt{x^2+1}}+1)+\log (x^2+1))=\frac{{\tanh }^{-1}\left(\frac{3\sqrt{x^2+1}+y(x)}{\sqrt{5}(\sqrt{x^2+1}+y(x))}\right)}{\sqrt{5}}+c_1,y(x)]$$ ✓ Maple : cpu = 0.438 (sec), leaf count = 115

dsolve(diff(y(x),x) = x/(y(x)+(x^2+1)^(1/2)),y(x))
 

$$-\frac{4\ln \left(\frac{36\sqrt{x^2+1}}{y\left(x\right)+\sqrt{x^2+1}}\right)}{3}+\frac{2\ln (-\frac{1296(\sqrt{x^2+1}y\left(x\right)-x^2+y{\left(x\right)}^2-1)}{11{(y\left(x\right)+\sqrt{x^2+1})}^2})}{3}-\frac{4\sqrt{5}\mathrm{arctanh}\left(\frac{(3\sqrt{x^2+1}+y\left(x\right))\sqrt{5}}{5y\left(x\right)+5\sqrt{x^2+1}}\right)}{15}+\frac{2\ln (x^2+1)}{3}-c_1=0$$