\[ -a+y(x) y''(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0630547 (sec), leaf count = 94
\[\left \{\left \{y(x)\to -\frac {\sqrt {2 a^2 c_2 x+a^2 c_2^2+a^2 x^2-e^{2 c_1}}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {2 a^2 c_2 x+a^2 c_2^2+a^2 x^2-e^{2 c_1}}}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.065 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) =\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}},y \left ( x \right ) =-\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}} \right \} \]