\[ \left (a x+\sqrt {y(x)^2+1}\right ) y'(x)+a y(x)+\sqrt {x^2+1}=0 \] ✓ Mathematica : cpu = 0.317301 (sec), leaf count = 53
\[\text {Solve}\left [a x y(x)+\frac {1}{2} \sqrt {x^2+1} x+\frac {1}{2} \left (y(x) \sqrt {y(x)^2+1}+\sinh ^{-1}(y(x))\right )+\frac {1}{2} \sinh ^{-1}(x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.037 (sec), leaf count = 41
\[\left \{a x y \left (x \right )+c_{1}+\frac {\sqrt {x^{2}+1}\, x}{2}+\frac {\arcsinh \left (x \right )}{2}+\frac {\arcsinh \left (y \left (x \right )\right )}{2}+\frac {\sqrt {y \left (x \right )^{2}+1}\, y \left (x \right )}{2} = 0\right \}\]