\[ y'(x)=\frac {a^2-a b y(x)-a b \sqrt {x}-b^2 x+b c}{a \left (a y(x)+a \sqrt {x}+b x-c\right )} \] ✓ Mathematica : cpu = 0.103769 (sec), leaf count = 625
DSolve[Derivative[1][y][x] == (a^2 + b*c - a*b*Sqrt[x] - b^2*x - a*b*y[x])/(a*(-c + a*Sqrt[x] + b*x + a*y[x])),y[x],x]
\[\left \{\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,1\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,2\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,3\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,4\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,5\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}+b x-c}{a}+\frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,6\right ]}\right \}\right \}\] ✓ Maple : cpu = 0.329 (sec), leaf count = 83
dsolve(diff(y(x),x) = -(b*y(x)*a-b*c+b^2*x+b*a*x^(1/2)-a^2)/a/(a*y(x)-c+b*x+a*x^(1/2)),y(x))
\[y \left (x \right ) = \frac {3 \tanh \left (\RootOf \left (-729 x^{3} \left (\tanh ^{6}\left (\textit {\_Z} \right )\right ) a^{6}+2187 x^{3} \left (\tanh ^{4}\left (\textit {\_Z} \right )\right ) a^{6}-2187 x^{3} \left (\tanh ^{2}\left (\textit {\_Z} \right )\right ) a^{6}+729 a^{6} x^{3}+64 c_{1} {\mathrm e}^{2 \textit {\_Z}}\right )\right ) \sqrt {x}\, a -a \sqrt {x}-2 b x +2 c}{2 a}\]