\[ \left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)-3 x y(x)^2+x=0 \] ✓ Mathematica : cpu = 0.0227355 (sec), leaf count = 518
\[\left \{\left \{y(x)\to \frac {1}{36} \left (-3 \sqrt [3]{3} \sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}-\frac {3\ 3^{2/3} \left (3 x^4-8\right )}{\sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}}+9 x^2\right )\right \},\left \{y(x)\to \frac {1}{24} \left (\sqrt [3]{3} \left (1-i \sqrt {3}\right ) \sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}+\frac {3^{2/3} \left (1+i \sqrt {3}\right ) \left (3 x^4-8\right )}{\sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}}+6 x^2\right )\right \},\left \{y(x)\to \frac {1}{24} \left (\sqrt [3]{3} \left (1+i \sqrt {3}\right ) \sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}+\frac {3^{2/3} \left (1-i \sqrt {3}\right ) \left (3 x^4-8\right )}{\sqrt [3]{4 \sqrt {3} \sqrt {-54 c_1 x^6+648 c_1 x^2+432 c_1^2-27 x^8+207 x^4+32}+144 c_1-9 x^6+108 x^2}}+6 x^2\right )\right \}\right \}\]
✓ Maple : cpu = 0.034 (sec), leaf count = 579
\[ \left \{ y \left ( x \right ) =-{\frac {1}{24} \left ( -6\,{x}^{2}\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}+ \left ( -9\,i{x}^{4}+i \left ( -324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96} \right ) ^{{\frac {2}{3}}}+24\,i \right ) \sqrt {3}+9\,{x}^{4}+ \left ( -324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96} \right ) ^{{\frac {2}{3}}}-24 \right ) {\frac {1}{\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}}}},y \left ( x \right ) ={\frac {1}{24} \left ( 6\,{x}^{2}\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}+ \left ( -9\,i{x}^{4}+i \left ( -324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96} \right ) ^{{\frac {2}{3}}}+24\,i \right ) \sqrt {3}-9\,{x}^{4}- \left ( -324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96} \right ) ^{{\frac {2}{3}}}+24 \right ) {\frac {1}{\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}}}},y \left ( x \right ) ={\frac {1}{12}\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}}+{\frac {3\,{x}^{4}-8}{4}{\frac {1}{\sqrt [3]{-324\,{x}^{2}-432\,{\it \_C1}+27\,{x}^{6}+12\,\sqrt {-81\,{x}^{8}-162\,{\it \_C1}\,{x}^{6}+621\,{x}^{4}+1944\,{x}^{2}{\it \_C1}+1296\,{{\it \_C1}}^{2}+96}}}}}+{\frac {{x}^{2}}{4}} \right \} \]