\[ a+2 y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0047571 (sec), leaf count = 31
DSolve[a - Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {x^2 \left (-a+c_1{}^2\right )}{4 c_2}+c_1 x+c_2\right \}\right \}\] ✓ Maple : cpu = 0.91 (sec), leaf count = 24
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+a=0,y(x))
\[y \left (x \right ) = \frac {\left (c_{1}^{2}-a \right ) x^{2}}{4 c_{2}}+c_{1} x +c_{2}\]