\[ \left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)-3 x y(x)^2+x=0 \] ✓ Mathematica : cpu = 0.276407 (sec), leaf count = 534
\[\left \{\left \{y(x)\to \frac {x^2}{4}-\frac {\sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{4\ 3^{2/3}}+\frac {6-\frac {9 x^4}{4}}{3 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \},\left \{y(x)\to \frac {x^2}{4}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{8\ 3^{2/3}}-\frac {\left (1+i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \},\left \{y(x)\to \frac {x^2}{4}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{8\ 3^{2/3}}-\frac {\left (1-i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 579
\[\left \{y \left (x \right ) = \frac {-9 x^{4}+6 \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}} x^{2}+\left (-9 i x^{4}+i \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {2}{3}}+24 i\right ) \sqrt {3}-\left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {2}{3}}+24}{24 \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}, y \left (x \right ) = -\frac {9 x^{4}-6 \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}} x^{2}+\left (-9 i x^{4}+i \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {2}{3}}+24 i\right ) \sqrt {3}+\left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {2}{3}}-24}{24 \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {x^{2}}{4}+\frac {\left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}{12}+\frac {3 x^{4}-8}{4 \left (27 x^{6}-324 x^{2}-432 c_{1}+12 \sqrt {-81 x^{8}-162 c_{1} x^{6}+621 x^{4}+1944 c_{1} x^{2}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}\right \}\]