\[ 2 (y(x)-a) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.344122 (sec), leaf count = 204
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {2} \left (\frac {1}{2} \sqrt {a-\text {$\#$1}} \sqrt {e^{2 c_1}-2 (a-\text {$\#$1})}-\frac {e^{2 c_1} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {a-\text {$\#$1}}}{\sqrt {e^{2 c_1}-2 (a-\text {$\#$1})}}\right )}{2 \sqrt {2}}\right )\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\sqrt {2} \left (\frac {1}{2} \sqrt {a-\text {$\#$1}} \sqrt {e^{2 c_1}-2 (a-\text {$\#$1})}-\frac {e^{2 c_1} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {a-\text {$\#$1}}}{\sqrt {e^{2 c_1}-2 (a-\text {$\#$1})}}\right )}{2 \sqrt {2}}\right )\& \right ]\left [c_2+x\right ]\right \}\right \}\] ✓ Maple : cpu = 0.581 (sec), leaf count = 117
\[ \left \{ -{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -a-{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }-x-{\it \_C2}+\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }=0,{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -a-{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }-x-{\it \_C2}-\sqrt {- \left ( -y \left ( x \right ) +a \right ) \left ( a+{\it \_C1}-y \left ( x \right ) \right ) }=0 \right \} \]