\[ y'(x)=\frac {y(x)^{3/2}}{x^2-2 x y(x)+y(x)^2+y(x)^{3/2}} \] ✓ Mathematica : cpu = 0.213749 (sec), leaf count = 2213
\[\left \{\left \{y(x)\to \frac {1}{3} \left (2 \left (x+e^{c_1}+2 e^{2 c_1}\right )-\sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {-x^2-2 e^{c_1} x-16 e^{3 c_1}-16 e^{4 c_1}+e^{2 c_1} (8 x-1)}{\sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (4 \left (x+e^{c_1}+2 e^{2 c_1}\right )+\left (1-i \sqrt {3}\right ) \sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {\left (1+i \sqrt {3}\right ) \left (x^2+2 e^{c_1} x+16 e^{3 c_1}+16 e^{4 c_1}+e^{2 c_1} (1-8 x)\right )}{\sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (4 \left (x+e^{c_1}+2 e^{2 c_1}\right )+\left (1+i \sqrt {3}\right ) \sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {\left (1-i \sqrt {3}\right ) \left (x^2+2 e^{c_1} x+16 e^{3 c_1}+16 e^{4 c_1}+e^{2 c_1} (1-8 x)\right )}{\sqrt [3]{x^3+3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x-96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)+e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {-e^{4 c_1} \left (x^3+3 e^{c_1} x^2-e^{2 c_1} (8 x-3) x+e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \},\left \{y(x)\to \frac {1}{3} \left (2 \left (x-e^{c_1}+2 e^{2 c_1}\right )-\sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {-x^2+2 e^{c_1} x+16 e^{3 c_1}-16 e^{4 c_1}+e^{2 c_1} (8 x-1)}{\sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (4 \left (x-e^{c_1}+2 e^{2 c_1}\right )+\left (1-i \sqrt {3}\right ) \sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {\left (1+i \sqrt {3}\right ) \left (x^2-2 e^{c_1} x-16 e^{3 c_1}+16 e^{4 c_1}+e^{2 c_1} (1-8 x)\right )}{\sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (4 \left (x-e^{c_1}+2 e^{2 c_1}\right )+\left (1+i \sqrt {3}\right ) \sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}+\frac {\left (1-i \sqrt {3}\right ) \left (x^2-2 e^{c_1} x-16 e^{3 c_1}+16 e^{4 c_1}+e^{2 c_1} (1-8 x)\right )}{\sqrt [3]{x^3-3 e^{c_1} x^2-3 e^{2 c_1} (4 x-1) x+96 e^{5 c_1}-64 e^{6 c_1}+6 e^{4 c_1} (8 x-5)-e^{3 c_1} (12 x+1)+6 \sqrt {3} \sqrt {e^{4 c_1} \left (-x^3+3 e^{c_1} x^2+e^{2 c_1} (8 x-3) x-e^{4 c_1} (16 x+1)+e^{3 c_1} (20 x+1)\right )}}}\right )\right \}\right \}\]
✓ Maple : cpu = 0.115 (sec), leaf count = 44
\[ \left \{ 2\,{\frac {\sqrt {y \left ( x \right ) }}{y \left ( x \right ) -x}}+ \left ( y \left ( x \right ) -x \right ) ^{-1}-2\,{\frac {x}{ \left ( y \left ( x \right ) -x \right ) \sqrt {y \left ( x \right ) }}}-{\it \_C1}=0 \right \} \]