\[ \boxed { 3\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -3\,x\ln \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{4}-y \left ( x \right ) =0} \]
Mathematica: cpu = 0.011001 (sec), leaf count = 115 \[ \left \{\left \{y(x)\to \frac {(-2)^{2/3} \sqrt [3]{x}}{\sqrt [3]{4 c_1+3 x^2-6 x^2 \log (x)}}\right \},\left \{y(x)\to \frac {2^{2/3} \sqrt [3]{x}}{\sqrt [3]{4 c_1+3 x^2-6 x^2 \log (x)}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3} \sqrt [3]{x}}{\sqrt [3]{4 c_1+3 x^2-6 x^2 \log (x)}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 234 \[ \left \{ y \left ( x \right ) ={\frac {1}{6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1}}\sqrt [3]{-4\,x \left ( 6\,{x}^{2} \ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1} \right ) ^{2}}},y \left ( x \right ) =-{\frac {1}{12\,{x}^{2}\ln \left ( x \right ) -6\,{x }^{2}-8\,{\it \_C1}}\sqrt [3]{-4\,x \left ( 6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1} \right ) ^{2}}}-{\frac {{\frac {i}{2 }}\sqrt {3}}{6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1} }\sqrt [3]{-4\,x \left ( 6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4 \,{\it \_C1} \right ) ^{2}}},y \left ( x \right ) =-{\frac {1}{12\,{x}^{2 }\ln \left ( x \right ) -6\,{x}^{2}-8\,{\it \_C1}}\sqrt [3]{-4\,x \left ( 6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1} \right ) ^{2}}}+{\frac {{\frac {i}{2}}\sqrt {3}}{6\,{x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1}}\sqrt [3]{-4\,x \left ( 6\, {x}^{2}\ln \left ( x \right ) -3\,{x}^{2}-4\,{\it \_C1} \right ) ^{2}}} \right \} \]