\[ y'(x)=\csc (x) \left (x^4 \log (2 x)-2 x^2 y(x) \log (2 x)+y(x)^2 \log (2 x)-\log (2 x)+2 x \sin (x)\right ) \] ✓ Mathematica : cpu = 12.3739 (sec), leaf count = 73
DSolve[Derivative[1][y][x] == Csc[x]*(-Log[2*x] + x^4*Log[2*x] + 2*x*Sin[x] - 2*x^2*Log[2*x]*y[x] + Log[2*x]*y[x]^2),y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x2 \csc (K[5]) \log (2 K[5])dK[5]\right )}{-\int _1^x\exp \left (\int _1^{K[6]}2 \csc (K[5]) \log (2 K[5])dK[5]\right ) \csc (K[6]) \log (2 K[6])dK[6]+c_1}+x^2+1\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(y(x),x) = (2*x*sin(x)-ln(2*x)+ln(2*x)*x^4-2*ln(2*x)*x^2*y(x)+ln(2*x)*y(x)^2)/sin(x),y(x))
, could not solve
dsolve(diff(y(x),x) = (2*x*sin(x)-ln(2*x)+ln(2*x)*x^4-2*ln(2*x)*x^2*y(x)+ln(2*x)*y(x)^2)/sin(x),y(x))