\[ \left (a x+\sqrt {y(x)^2+1}\right ) y'(x)+a y(x)+\sqrt {x^2+1}=0 \] ✓ Mathematica : cpu = 0.0752833 (sec), leaf count = 43
\[\text {Solve}\left [y(x) \left (2 a x+\sqrt {y(x)^2+1}\right )+\sqrt {x^2+1} x+\sinh ^{-1}(y(x))+\sinh ^{-1}(x)=2 c_1,y(x)\right ]\]
✓ Maple : cpu = 0.039 (sec), leaf count = 41
\[ \left \{ {\frac {x}{2}\sqrt {{x}^{2}+1}}+{\frac {{\it Arcsinh} \left ( x \right ) }{2}}+axy \left ( x \right ) +{\frac {y \left ( x \right ) }{2}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+1}}+{\frac {{\it Arcsinh} \left ( y \left ( x \right ) \right ) }{2}}+{\it \_C1}=0 \right \} \]