\[ 2 (y(x)-a) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.668804 (sec), leaf count = 251
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 \sqrt {a-\text {$\#$1}} \left (2 \text {$\#$1}-2 a+e^{2 c_1}\right )-\sqrt {2} e^{3 c_1} \sqrt {e^{-2 c_1} \left (2 \text {$\#$1}-2 a+e^{2 c_1}\right )} \sin ^{-1}\left (\sqrt {2} e^{-c_1} \sqrt {a-\text {$\#$1}}\right )}{2 \sqrt {2} \sqrt {2 \text {$\#$1}-2 a+e^{2 c_1}}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 \sqrt {a-\text {$\#$1}} \left (2 \text {$\#$1}-2 a+e^{2 c_1}\right )-\sqrt {2} e^{3 c_1} \sqrt {e^{-2 c_1} \left (2 \text {$\#$1}-2 a+e^{2 c_1}\right )} \sin ^{-1}\left (\sqrt {2} e^{-c_1} \sqrt {a-\text {$\#$1}}\right )}{2 \sqrt {2} \sqrt {2 \text {$\#$1}-2 a+e^{2 c_1}}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.424 (sec), leaf count = 117
\[ \left \{ -{\frac {{\it \_C1}}{2}\arctan \left ( { \left ( y \left ( x \right ) -a-{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }-x-{\it \_C2}+\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }=0,{\frac {{\it \_C1}}{2}\arctan \left ( { \left ( y \left ( x \right ) -a-{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }-x-{\it \_C2}-\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }=0 \right \} \]