\[ y'(x)=\frac {-a^2-a b y(x)-a b \sqrt {x}+a b+b^2 x+b^2}{a \left (a (-y(x))-a \sqrt {x}+a+b x+b\right )} \] ✓ Mathematica : cpu = 0.0748753 (sec), leaf count = 649
DSolve[Derivative[1][y][x] == (-a^2 + a*b + b^2 - a*b*Sqrt[x] + b^2*x - a*b*y[x])/(a*(a + b - a*Sqrt[x] + b*x - a*y[x])),y[x],x]
\[\left \{\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,1\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,2\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,3\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,4\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,5\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,6\right ]}\right \}\right \}\] ✓ Maple : cpu = 0.395 (sec), leaf count = 116
dsolve(diff(y(x),x) = (-b*y(x)*a+b^2+a*b+b^2*x-b*a*x^(1/2)-a^2)/a/(-a*y(x)+b+a+b*x-a*x^(1/2)),y(x))
\[y \left (x \right ) = \frac {\operatorname {RootOf}\left (-x^{\frac {3}{2}} a b +b^{2} x^{2}-a^{2} \sqrt {x}-b a \sqrt {x}-2 a^{2} x +2 a b x +2 b^{2} x +a^{2}+2 a b +b^{2}+{\mathrm e}^{\operatorname {RootOf}\left (9 x \tanh \left (-\frac {3 \textit {\_Z}}{2}+\frac {c_{1}}{2}\right )^{2} a^{2}-9 a^{2} x +4 \,{\mathrm e}^{\textit {\_Z}}\right )}+\left (a \sqrt {x}-2 b x -2 a -2 b \right ) \textit {\_Z} +\textit {\_Z}^{2}\right )}{a}\]