\[ \left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)-3 x y(x)^2+x=0 \] ✓ Mathematica : cpu = 0.233917 (sec), leaf count = 534
DSolve[x - 3*x*y[x]^2 + (1 - 3*x^2*y[x] + 6*y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {x^2}{4}-\frac {\sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{4\ 3^{2/3}}+\frac {6-\frac {9 x^4}{4}}{3 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \},\left \{y(x)\to \frac {x^2}{4}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{8\ 3^{2/3}}-\frac {\left (1+i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \},\left \{y(x)\to \frac {x^2}{4}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}{8\ 3^{2/3}}-\frac {\left (1-i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6 \sqrt [3]{3} \sqrt [3]{-9 x^6+108 x^2+4 \sqrt {3} \sqrt {-27 x^8-54 c_1 x^6+207 x^4+648 c_1 x^2+32+432 c_1{}^2}+144 c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.036 (sec), leaf count = 579
dsolve((6*y(x)^2-3*x^2*y(x)+1)*diff(y(x),x)-3*x*y(x)^2+x = 0,y(x))
\[y \left (x \right ) = \frac {\left (-324 x^{2}-432 c_{1}+27 x^{6}+12 \sqrt {-81 x^{8}-162 x^{6} c_{1}+621 x^{4}+1944 x^{2} c_{1}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}{12}+\frac {3 x^{4}-8}{4 \left (-324 x^{2}-432 c_{1}+27 x^{6}+12 \sqrt {-81 x^{8}-162 x^{6} c_{1}+621 x^{4}+1944 x^{2} c_{1}+1296 c_{1}^{2}+96}\right )^{\frac {1}{3}}}+\frac {x^{2}}{4}\]