\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac { \left ( -108\,{x}^{3/2}-216-216\, \left ( y \left ( x \right ) \right ) ^{2}+72\,{x}^{3}y \left ( x \right ) -6\,{x}^{6}-216\, \left ( y \left ( x \right ) \right ) ^{3}+108\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}-18\,y \left ( x \right ) {x}^{6}+{x}^{9} \right ) \sqrt {x}}{216}}=0} \]
Mathematica: cpu = 0.068009 (sec), leaf count = 119 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {1}{2} \left (2 \sqrt {x}-x^{7/2}\right )+3 \sqrt {x} y(x)}{\sqrt [3]{29} \sqrt [3]{x^{3/2}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {2}{27} 29^{2/3} \sqrt {x} \left (x^{3/2}\right )^{2/3},y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}}{6}}-{\frac {1}{3}}+{ \frac {29}{9}{\it RootOf} \left ( 2\,{x}^{3/2}-243\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a} }+9\,{\it \_C1} \right ) } \right \} \]