\[ y'(x)=\frac {a^2-a b y(x)-a b \sqrt {x}-b^2 x+b c}{a \left (a y(x)+a \sqrt {x}+b x-c\right )} \] ✓ Mathematica : cpu = 0.0750291 (sec), leaf count = 625
\[\left \{\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,1\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \},\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,2\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \},\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,3\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \},\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,4\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \},\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,5\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \},\left \{y(x)\to \frac {1}{a^2 \text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-\frac {24 \text {$\#$1}^4 x^2}{a^4}+\frac {8 \text {$\#$1}^3 x^{3/2}}{a^6}+\frac {9 \text {$\#$1}^2 x}{a^8}-\frac {6 \text {$\#$1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,6\right ]}-\frac {a \sqrt {x}+b x-c}{a}\right \}\right \}\]
✓ Maple : cpu = 0.344 (sec), leaf count = 138
\[ \left \{ 9\,{\frac {1}{ \left ( \sqrt {x}{a}^{2}y \left ( x \right ) +{x}^{3/2}ab+{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+2\,abxy \left ( x \right ) +{b}^{2}{x}^{2}-\sqrt {x}ac-2\,{a}^{2}x-2\,cay \left ( x \right ) -2\,bcx+{c}^{2} \right ) ^{3}} \left ( 1/3\,{\frac {2\,ay \left ( x \right ) +a\sqrt {x}+2\,bx-2\,c}{a\sqrt {x}}}+1 \right ) ^{2} \left ( 9-{\frac { \left ( 2\,ay \left ( x \right ) +a\sqrt {x}+2\,bx-2\,c \right ) ^{2}}{{a}^{2}x}} \right ) ^{-1}}-{\it \_C1}=0 \right \} \]