\[ a-y'(x)^2+2 y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0043131 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {x^2 \left (-a+c_1{}^2\right )}{4 c_2}+c_1 x+c_2\right \}\right \}\] ✓ Maple : cpu = 0.191 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {{\it \_C1}}^{2}-a \right ) {x}^{2}}{4\,{\it \_C2}}}+{\it \_C1}\,x+{\it \_C2} \right \} \]