\[ y'(x)=\frac {\frac {24}{5} x^{7/2} y(x)-\frac {24 x^{13/2}}{25}+\frac {8 x^{7/2}}{5}-8 x^{3/2}-\frac {8 x^9}{125}+\frac {12}{25} x^6 y(x)+\frac {4 x^6}{25}-\frac {24 x^4}{5}-\frac {6}{5} x^3 y(x)^2-\frac {4}{5} x^3 y(x)+\frac {6 x^3}{5}+12 x y(x)-6 \sqrt {x} y(x)^2-4 \sqrt {x} y(x)+y(x)^3+y(x)^2+4 x+\sqrt {x}+1}{x} \] ✓ Mathematica : cpu = 0.349102 (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 = 0.085 (sec), leaf count = 53
\[y \relax (x ) = \frac {18 x^{\frac {7}{2}}+145 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \relax (x )+3 c_{1}\right ) \sqrt {x}-15 \sqrt {x}+90 x}{45 \sqrt {x}}\]