\[ y'(x)=\frac {\frac {12}{25} x^6 y(x)+\frac {24}{5} x^{7/2} y(x)-\frac {6}{5} x^3 y(x)^2-\frac {4}{5} x^3 y(x)-\frac {8 x^9}{125}-\frac {24 x^{13/2}}{25}+\frac {4 x^6}{25}-\frac {24 x^4}{5}+\frac {8 x^{7/2}}{5}+\frac {6 x^3}{5}-8 x^{3/2}+12 x y(x)-6 \sqrt {x} y(x)^2-4 \sqrt {x} y(x)+y(x)^3+y(x)^2+4 x+\sqrt {x}+1}{x} \] ✓ Mathematica : cpu = 0.357118 (sec), leaf count = 115
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {-6 x^3-30 \sqrt {x}+5}{5 x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.177 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\frac {1}{45} \left ( 18\,{x}^{7/2}+145\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( x \right ) +3\,{\it \_C1} \right ) \sqrt {x}-15\,\sqrt {x}+90\,x \right ) {\frac {1}{\sqrt {x}}}} \right \} \]