\[ -a+y(x) y''(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.182406 (sec), leaf count = 94
DSolve[-a + Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.894 (sec), leaf count = 39
dsolve(diff(diff(y(x),x),x)*y(x)+diff(y(x),x)^2-a=0,y(x))
\[y \left (x \right ) = \sqrt {a \,x^{2}-2 c_{1} x +2 c_{2}}\]