\[ A x \left (a \sin ^2(x)+c\right )+y'(x) \left (a \sin ^2(x)+b\right )+a y(x) \sin (2 x)=0 \] ✓ Mathematica : cpu = 0.128949 (sec), leaf count = 77
DSolve[A*x*(c + a*Sin[x]^2) + a*Sin[2*x]*y[x] + (b + a*Sin[x]^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\frac {1}{2} a A x^2-\frac {1}{2} a A x \sin (2 x)-\frac {1}{4} a A \cos (2 x)+A c x^2}{a \cos (2 x)-a-2 b}+\frac {c_1}{a \cos (2 x)-a-2 b}\right \}\right \}\] ✓ Maple : cpu = 0.094 (sec), leaf count = 53
dsolve((a*sin(x)^2+b)*diff(y(x),x)+a*y(x)*sin(2*x)+A*x*(a*sin(x)^2+c) = 0,y(x))
\[y \left (x \right ) = \frac {-A a \cos \left (2 x \right )-2 A x a \sin \left (2 x \right )+2 x^{2} \left (a +2 c \right ) A -8 c_{1}}{4 a \cos \left (2 x \right )-4 a -8 b}\]