\[ y'(x)=\frac {\left (-y(x)+\sqrt {y(x)}+x\right ) y(x)^{3/2}}{x^3-3 x^2 y(x)+3 x y(x)^2+x y(x)^{3/2}-y(x)^3-y(x)^{5/2}+y(x)^2} \] ✓ Mathematica : cpu = 0.220941 (sec), leaf count = 251
DSolve[Derivative[1][y][x] == ((x + Sqrt[y[x]] - y[x])*y[x]^(3/2))/(x^3 - 3*x^2*y[x] + x*y[x]^(3/2) + y[x]^2 + 3*x*y[x]^2 - y[x]^(5/2) - y[x]^3),y[x],x]
\[\left \{\left \{y(x)\to \text {Root}\left [\text {$\#$1}^9 c_1{}^4-6 \text {$\#$1}^8 c_1{}^4 x+\text {$\#$1}^7 \left (15 c_1{}^4 x^2-6 c_1{}^2\right )+\text {$\#$1}^6 \left (-20 c_1{}^4 x^3+30 c_1{}^2 x-4+2 c_1{}^2\right )+\text {$\#$1}^5 \left (15 c_1{}^4 x^4-60 c_1{}^2 x^2+24 x-6 c_1{}^2 x+9\right )+\text {$\#$1}^4 \left (-6 c_1{}^4 x^5+60 c_1{}^2 x^3-60 x^2+6 c_1{}^2 x^2-36 x-6\right )+\text {$\#$1}^3 \left (c_1{}^4 x^6-30 c_1{}^2 x^4+80 x^3-2 c_1{}^2 x^3+54 x^2+12 x+1\right )+\text {$\#$1}^2 \left (6 c_1{}^2 x^5-60 x^4-36 x^3-6 x^2\right )+\text {$\#$1} \left (24 x^5+9 x^4\right )-4 x^6\& ,1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.122 (sec), leaf count = 193
dsolve(diff(y(x),x) = y(x)^(3/2)*(x-y(x)+y(x)^(1/2))/(y(x)^(3/2)*x-y(x)^(5/2)+y(x)^2+x^3-3*x^2*y(x)+3*x*y(x)^2-y(x)^3),y(x))
\[-\frac {\left (x^{6} c_{1}+80 x^{3}-54 x^{2}-12 x -1\right ) y \left (x \right )^{\frac {11}{2}}+\left (-6 x^{5} c_{1}-60 x^{2}+36 x +6\right ) y \left (x \right )^{\frac {13}{2}}+\left (15 c_{1} x^{4}+24 x -9\right ) y \left (x \right )^{\frac {15}{2}}+\left (-60 x^{4}+36 x^{3}+6 x^{2}\right ) y \left (x \right )^{\frac {9}{2}}+\left (-20 x^{3} c_{1}-4\right ) y \left (x \right )^{\frac {17}{2}}+\left (24 x^{5}-9 x^{4}\right ) y \left (x \right )^{\frac {7}{2}}+15 y \left (x \right )^{\frac {19}{2}} c_{1} x^{2}-6 y \left (x \right )^{\frac {21}{2}} c_{1} x +y \left (x \right )^{\frac {23}{2}} c_{1}-4 x^{6} y \left (x \right )^{\frac {5}{2}}+12 y \left (x \right )^{3} \left (x -y \left (x \right )\right )^{3} \left (y \left (x \right )^{2}+\left (-2 x -\frac {1}{3}\right ) y \left (x \right )+x^{2}\right )}{y \left (x \right )^{\frac {11}{2}} \left (x -y \left (x \right )\right )^{6}} = 0\]