\[ \left (\text {Global$\grave { }$a} \text {Global$\grave { }$x}+\sqrt {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+1}\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\sqrt {\text {Global$\grave { }$x}^2+1}=0 \] ✓ Mathematica : cpu = 0.0613316 (sec), leaf count = 53
\[\text {Solve}\left [\text {Global$\grave { }$a} \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\frac {1}{2} \sqrt {\text {Global$\grave { }$x}^2+1} \text {Global$\grave { }$x}+\frac {1}{2} \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \sqrt {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+1}+\sinh ^{-1}(\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))\right )+\frac {1}{2} \sinh ^{-1}(\text {Global$\grave { }$x})=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\]
✓ Maple : cpu = 0.033 (sec), leaf count = 41
\[ \left \{ {\frac {x}{2}\sqrt {{x}^{2}+1}}+{\frac {{\it Arcsinh} \left ( x \right ) }{2}}+axy \left ( x \right ) +{\frac {y \left ( x \right ) }{2}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+1}}+{\frac {{\it Arcsinh} \left ( y \left ( x \right ) \right ) }{2}}+{\it \_C1}=0 \right \} \]