\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac {by \left ( x \right ) a-bc+{b}^{2}x+ba\sqrt {x}-{a}^{2}}{a \left ( ay \left ( x \right ) -c+bx+a\sqrt {x} \right ) }}=0} \]
Mathematica: cpu = 0.082010 (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 = 0.202 (sec), leaf count = 83 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,a} \left ( 3\,\tanh \left ( { \it RootOf} \left ( -729\,{x}^{3} \left ( \tanh \left ( {\it \_Z} \right ) \right ) ^{6}{a}^{6}+2187\,{x}^{3} \left ( \tanh \left ( {\it \_Z} \right ) \right ) ^{4}{a}^{6}-2187\,{x}^{3} \left ( \tanh \left ( { \it \_Z} \right ) \right ) ^{2}{a}^{6}+729\,{a}^{6}{x}^{3}+64\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it \_C1} \right ) \right ) a\sqrt { x}-a\sqrt {x}-2\,bx+2\,c \right ) } \right \} \]