\[ a+x y'(x)^2-2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.282294 (sec), leaf count = 777
DSolve[a - 2*y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{4} a^2 e^{-\frac {3 c_1}{2}} x^2+\frac {1}{4} e^{-\frac {3 c_1}{2}} \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}-\frac {e^{-\frac {3 c_1}{2}} \left (-9 a^4 x^4-72 a e^{3 c_1} x\right )}{36 \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}}\right \},\left \{y(x)\to \frac {1}{4} a^2 e^{-\frac {3 c_1}{2}} x^2-\frac {1}{8} \left (1-i \sqrt {3}\right ) e^{-\frac {3 c_1}{2}} \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}+\frac {\left (1+i \sqrt {3}\right ) e^{-\frac {3 c_1}{2}} \left (-9 a^4 x^4-72 a e^{3 c_1} x\right )}{72 \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}}\right \},\left \{y(x)\to \frac {1}{4} a^2 e^{-\frac {3 c_1}{2}} x^2-\frac {1}{8} \left (1+i \sqrt {3}\right ) e^{-\frac {3 c_1}{2}} \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}+\frac {\left (1-i \sqrt {3}\right ) e^{-\frac {3 c_1}{2}} \left (-9 a^4 x^4-72 a e^{3 c_1} x\right )}{72 \sqrt [3]{a^6 x^6-20 a^3 e^{3 c_1} x^3+8 \sqrt {-a^9 e^{3 c_1} x^9+3 a^6 e^{6 c_1} x^6-3 a^3 e^{9 c_1} x^3+e^{12 c_1}}-8 e^{6 c_1}}}\right \}\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 689
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+a = 0,y(x))
\[y \left (x \right ) = \frac {x \left (\frac {4 x^{2}}{\left (-36 a c_{1}^{2}+8 x^{3}+12 \sqrt {a \left (9 a c_{1}^{2}-4 x^{3}\right )}\, c_{1}\right )^{\frac {1}{3}}}+2 x +\left (-36 a c_{1}^{2}+8 x^{3}+12 \sqrt {a \left (9 a c_{1}^{2}-4 x^{3}\right )}\, c_{1}\right )^{\frac {1}{3}}\right )}{12 c_{1}}+\frac {3 a c_{1}}{\frac {4 x^{2}}{\left (-36 a c_{1}^{2}+8 x^{3}+12 \sqrt {a \left (9 a c_{1}^{2}-4 x^{3}\right )}\, c_{1}\right )^{\frac {1}{3}}}+2 x +\left (-36 a c_{1}^{2}+8 x^{3}+12 \sqrt {a \left (9 a c_{1}^{2}-4 x^{3}\right )}\, c_{1}\right )^{\frac {1}{3}}}\]