\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) +{x}^{3}\ln \left ( x \right ) +{x}^{4}+{x}^{3}+7\,x \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( x \right ) +7\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+7\,x \left ( y \left ( x \right ) \right ) ^{2}}{x}}=0} \]
Mathematica: cpu = 0.035505 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to \frac {x \tan \left (\frac {1}{12} \left (12 \sqrt {7} c_1+4 \sqrt {7} x^3+3 \sqrt {7} x^2+6 \sqrt {7} x^2 \log (x)\right )\right )}{\sqrt {7}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\frac {x\sqrt {7}}{7}\tan \left ( {\frac { \left ( 6\,{x}^{2}\ln \left ( x \right ) +4\,{x}^{3}+3\,{x}^{2}+12\,{ \it \_C1} \right ) \sqrt {7}}{12}} \right ) } \right \} \]