\[ \text {Global$\grave { }$a} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$x}=0 \] ✓ Mathematica : cpu = 0.960769 (sec), leaf count = 53
\[\text {Solve}\left [\left \{\text {Global$\grave { }$x}=\frac {c_1 \text {K$\$$1861292}}{\sqrt {1-\text {K$\$$1861292}^2}}+\frac {\text {Global$\grave { }$a} \text {K$\$$1861292} \sin ^{-1}(\text {K$\$$1861292})}{\sqrt {1-\text {K$\$$1861292}^2}},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=\frac {\text {Global$\grave { }$x}}{\text {K$\$$1861292}}-\text {Global$\grave { }$a} \text {K$\$$1861292}\right \},\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x}),\text {K$\$$1861292}\}\right ]\]
✓ Maple : cpu = 0.216 (sec), leaf count = 379
\[ \left \{ -{{\it \_C1} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {{\frac {1}{a} \left ( 2\,a-y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}{\frac {1}{\sqrt {{\frac {1}{a} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,a \right ) }}}}}+x+{1 \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \ln \left ( {\frac {1}{2\,a} \left ( \sqrt {{\frac {1}{{a}^{2}} \left ( 4\,ax+2\, \left ( y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-4\,{a}^{2} \right ) }}a+\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-y \left ( x \right ) \right ) } \right ) {\frac {1}{\sqrt {-2\,{\frac {y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+2\,{a}^{2}-2\,ax- \left ( y \left ( x \right ) \right ) ^{2}}{{a}^{2}}}}}}}=0,{{\it \_C1} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {{\frac {1}{a} \left ( 4\,a-2\,y \left ( x \right ) -2\,\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}{\frac {1}{\sqrt {{\frac {1}{a} \left ( -2\,y \left ( x \right ) -2\,\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-4\,a \right ) }}}}}+x-{\frac {\sqrt {2}}{2} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \ln \left ( {\frac {1}{2\,a} \left ( \sqrt {2}\sqrt {{\frac {1}{{a}^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }}a-\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-y \left ( x \right ) \right ) } \right ) {\frac {1}{\sqrt {{\frac {1}{{a}^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}=0 \right \} \]