\[ 2 (y(x)-a) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.779245 (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 = 1.778 (sec), leaf count = 117
\[\left \{-\frac {c_{1} \arctan \left (\frac {-\frac {c_{1}}{2}-a +y \left (x \right )}{\sqrt {-\left (a -y \left (x \right )\right ) \left (c_{1}+a -y \left (x \right )\right )}}\right )}{2}-c_{2}-x +\sqrt {-\left (a -y \left (x \right )\right ) \left (c_{1}+a -y \left (x \right )\right )} = 0, \frac {c_{1} \arctan \left (\frac {-\frac {c_{1}}{2}-a +y \left (x \right )}{\sqrt {-\left (a -y \left (x \right )\right ) \left (c_{1}+a -y \left (x \right )\right )}}\right )}{2}-c_{2}-x -\sqrt {-\left (a -y \left (x \right )\right ) \left (c_{1}+a -y \left (x \right )\right )} = 0\right \}\]