\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {150\,{x}^{3}+125\,\sqrt {x}+125+125\, \left ( y \left ( x \right ) \right ) ^{2}-100\,{x}^{3}y \left ( x \right ) -500\,y \left ( x \right ) \sqrt {x}+20\,{x}^{6}+200\,{x}^{7/2}+500\,x+125\, \left ( y \left ( x \right ) \right ) ^{3}-150\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}-750\, \left ( y \left ( x \right ) \right ) ^{2}\sqrt {x}+60\,y \left ( x \right ) {x}^{6}+600\,y \left ( x \right ) {x}^{7/2}+1500\,xy \left ( x \right ) -8\,{x}^{9}-120\,{x}^{13/2}-600\,{x}^{4}-1000\,{x}^{3/2}}{125\,x}}=0} \]
Mathematica: cpu = 0.087511 (sec), leaf count = 115 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {-6 x^3-30 \sqrt {x}+5}{5 x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x),y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\frac {1}{45} \left ( 18\,{x}^{7/2}+145\, {\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{ 3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( x \right ) +3 \,{\it \_C1} \right ) \sqrt {x}-15\,\sqrt {x}+90\,x \right ) {\frac {1}{ \sqrt {x}}}} \right \} \]