\[ y'(x) (-a y(x)+b x+c)+a x y'(x)^2-b y(x)=0 \] ✗ Mathematica : cpu = 3629.45 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.072 (sec), leaf count = 85
\[ \left \{ y \left ( x \right ) ={\frac {1}{a} \left ( -bx+c-2\,\sqrt {-bcx} \right ) },y \left ( x \right ) ={\frac {1}{a} \left ( -bx+c+2\,\sqrt {-bcx} \right ) },y \left ( x \right ) =-{\frac { \left ( a{{\it \_C1}}^{2}+{\it \_C1}\,b \right ) x}{-{\it \_C1}\,a-b}}-{\frac {c{\it \_C1}}{-{\it \_C1}\,a-b}} \right \} \]