\[ y'(x)^2+2 x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.15208 (sec), leaf count = 1193
DSolve[-y[x] + 2*x*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {x^2}{4}+\frac {1}{4} \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}-\frac {-9 x^4-72 e^{3 c_1} x}{36 \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \},\left \{y(x)\to -\frac {x^2}{4}-\frac {1}{8} \left (1-i \sqrt {3}\right ) \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}+\frac {\left (1+i \sqrt {3}\right ) \left (-9 x^4-72 e^{3 c_1} x\right )}{72 \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \},\left \{y(x)\to -\frac {x^2}{4}-\frac {1}{8} \left (1+i \sqrt {3}\right ) \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}+\frac {\left (1-i \sqrt {3}\right ) \left (-9 x^4-72 e^{3 c_1} x\right )}{72 \sqrt [3]{-x^6+20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {-e^{3 c_1} x^9+3 e^{6 c_1} x^6-3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \},\left \{y(x)\to -\frac {x^2}{4}+\frac {1}{4} \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}-\frac {72 e^{3 c_1} x-9 x^4}{36 \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \},\left \{y(x)\to -\frac {x^2}{4}-\frac {1}{8} \left (1-i \sqrt {3}\right ) \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}+\frac {\left (1+i \sqrt {3}\right ) \left (72 e^{3 c_1} x-9 x^4\right )}{72 \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \},\left \{y(x)\to -\frac {x^2}{4}-\frac {1}{8} \left (1+i \sqrt {3}\right ) \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}+\frac {\left (1-i \sqrt {3}\right ) \left (72 e^{3 c_1} x-9 x^4\right )}{72 \sqrt [3]{-x^6-20 e^{3 c_1} x^3+8 e^{6 c_1}+8 \sqrt {e^{3 c_1} x^9+3 e^{6 c_1} x^6+3 e^{9 c_1} x^3+e^{12 c_1}}}}\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 589
dsolve(diff(y(x),x)^2+2*x*diff(y(x),x)-y(x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (\frac {x^{2}}{\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}}-x +\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}\right )^{2}}{4}+x \left (\frac {x^{2}}{\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}}-x +\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}\right )\]