\[ -a+y'(x)^2+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.16745 (sec), leaf count = 94
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.188 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) =\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}},y \left ( x \right ) =-\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}} \right \} \]