\[ y'(x)=\frac {-y(x)+\sqrt {y(x)}+x}{-y(x)+\sqrt {y(x)}+x+1} \] ✓ Mathematica : cpu = 0.169144 (sec), leaf count = 943
\[\left \{\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {$\#$1}^6+(-6 x-6) \text {$\#$1}^5+\left (15 x^2+24 x+9\right ) \text {$\#$1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {$\#$1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {$\#$1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {$\#$1}\& ,6\right ]\right \}\right \}\] ✓ Maple : cpu = 0.098 (sec), leaf count = 44
\[-2 y \relax (x )^{\frac {3}{2}}+y \relax (x )^{3}+\left (-3 x -3\right ) y \relax (x )^{2}+\left (3 x^{2}+3 x \right ) y \relax (x )-x^{3}-c_{1} = 0\]