\[ y'(x)=\frac {\frac {24}{5} x^{7/2} y(x)-\frac {24 x^{13/2}}{25}+\frac {8 x^{7/2}}{5}-8 x^{3/2}-\frac {8 x^9}{125}+\frac {12}{25} x^6 y(x)+\frac {4 x^6}{25}-\frac {24 x^4}{5}-\frac {6}{5} x^3 y(x)^2-\frac {4}{5} x^3 y(x)+\frac {6 x^3}{5}+12 x y(x)-6 \sqrt {x} y(x)^2-4 \sqrt {x} y(x)+y(x)^3+y(x)^2+4 x+\sqrt {x}+1}{x} \] ✓ Mathematica : cpu = 0.349102 (sec), leaf count = 115
DSolve[Derivative[1][y][x] == (1 + Sqrt[x] + 4*x - 8*x^(3/2) + (6*x^3)/5 + (8*x^(7/2))/5 - (24*x^4)/5 + (4*x^6)/25 - (24*x^(13/2))/25 - (8*x^9)/125 - 4*Sqrt[x]*y[x] + 12*x*y[x] - (4*x^3*y[x])/5 + (24*x^(7/2)*y[x])/5 + (12*x^6*y[x])/25 + y[x]^2 - 6*Sqrt[x]*y[x]^2 - (6*x^3*y[x]^2)/5 + y[x]^3)/x,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {-6 x^3-30 \sqrt {x}+5}{5 x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.085 (sec), leaf count = 53
dsolve(diff(y(x),x) = 1/125*(150*x^3+125*x^(1/2)+125+125*y(x)^2-100*x^3*y(x)-500*y(x)*x^(1/2)+20*x^6+200*x^(7/2)+500*x+125*y(x)^3-150*x^3*y(x)^2-750*y(x)^2*x^(1/2)+60*y(x)*x^6+600*y(x)*x^(7/2)+1500*x*y(x)-8*x^9-120*x^(13/2)-600*x^4-1000*x^(3/2))/x,y(x))
\[y \left (x \right ) = \frac {18 x^{\frac {7}{2}}+145 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1}\right ) \sqrt {x}-15 \sqrt {x}+90 x}{45 \sqrt {x}}\]