\[ y'(x)^2+2 x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.369751 (sec), leaf count = 1757
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 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}+\frac {-9 x^4-72 \cosh (3 c_1) x-72 \sinh (3 c_1) x}{36 \sqrt [3]{x^6-20 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (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 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}-\frac {\left (1+i \sqrt {3}\right ) \left (-9 x^4-72 \cosh (3 c_1) x-72 \sinh (3 c_1) x\right )}{72 \sqrt [3]{x^6-20 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (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 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}-\frac {\left (1-i \sqrt {3}\right ) \left (-9 x^4-72 \cosh (3 c_1) x-72 \sinh (3 c_1) x\right )}{72 \sqrt [3]{x^6-20 \cosh (3 c_1) x^3-20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {-\cosh (3 c_1) x^9-\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6-3 \cosh (9 c_1) x^3-3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}}\right \},\left \{y(x)\to -\frac {x^2}{4}-\frac {1}{4} \sqrt [3]{x^6+20 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}+\frac {-9 x^4+72 \cosh (3 c_1) x+72 \sinh (3 c_1) x}{36 \sqrt [3]{x^6+20 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (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 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}-\frac {\left (1+i \sqrt {3}\right ) \left (-9 x^4+72 \cosh (3 c_1) x+72 \sinh (3 c_1) x\right )}{72 \sqrt [3]{x^6+20 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (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 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}-\frac {\left (1-i \sqrt {3}\right ) \left (-9 x^4+72 \cosh (3 c_1) x+72 \sinh (3 c_1) x\right )}{72 \sqrt [3]{x^6+20 \cosh (3 c_1) x^3+20 \sinh (3 c_1) x^3-8 \cosh (6 c_1)-8 \sinh (6 c_1)+8 \sqrt {\cosh (3 c_1) x^9+\sinh (3 c_1) x^9+3 \cosh (6 c_1) x^6+3 \sinh (6 c_1) x^6+3 \cosh (9 c_1) x^3+3 \sinh (9 c_1) x^3+\cosh (12 c_1)+\sinh (12 c_1)}}}\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 619
dsolve(diff(y(x),x)^2+2*x*diff(y(x),x)-y(x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (\frac {x^{2}}{\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}}-x +\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}\right )^{2}}{4}+x \left (\frac {x^{2}}{\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}}-x +\left (6 c_{1}-x^{3}+2 \sqrt {-3 x^{3} c_{1}+9 c_{1}^{2}}\right )^{\frac {1}{3}}\right )\]