\[ y'(x)-\sqrt {\frac {a y(x)^2+b y(x)+c}{a x^2+b x+c}}=0 \] ✓ Mathematica : cpu = 0.175228 (sec), leaf count = 90
\[\left \{\left \{y(x)\to \frac {e^{-\sqrt {a} c_1} \left (2 \sqrt {a} \left (e^{2 \sqrt {a} c_1}-1\right ) \sqrt {x (a x+b)+c}+b \left (e^{\sqrt {a} c_1}-1\right ){}^2+2 a x \left (e^{2 \sqrt {a} c_1}+1\right )\right )}{4 a}\right \}\right \}\]
✓ Maple : cpu = 0.082 (sec), leaf count = 124
\[ \left \{ -{1\sqrt {{\frac {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}{a{x}^{2}+bx+c}}}\sqrt {a{x}^{2}+bx+c}\ln \left ( {\frac {1}{2} \left ( 2\,\sqrt {a{x}^{2}+bx+c}\sqrt {a}+2\,ax+b \right ) {\frac {1}{\sqrt {a}}}} \right ) {\frac {1}{\sqrt {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}}}{\frac {1}{\sqrt {a}}}}+{1\ln \left ( \sqrt {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}+{\frac {2\,ay \left ( x \right ) +b}{2}{\frac {1}{\sqrt {a}}}} \right ) {\frac {1}{\sqrt {a}}}}+{\it \_C1}=0 \right \} \]