ODE
\[ y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0606009 (sec), leaf count = 81
\[\left \{\left \{y(x)\to \csc (x) \sec (x) \left (c_1+4 i \text {Li}_2\left (-i e^{i x}\right )-4 i \text {Li}_2\left (i e^{i x}\right )+4 x \log \left (1-i e^{i x}\right )-4 x \log \left (1+i e^{i x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 1.581 (sec), leaf count = 99
\[ \left \{ y \left ( x \right ) =-16\, \left ( \sin \left ( 2\,x \right ) \left ( i{\it dilog} \left ( 1-i{{\rm e}^{ix}} \right ) -i{\it dilog} \left ( 1+i{{\rm e}^{ix}} \right ) -x\ln \left ( 1-i{{\rm e}^{ix}} \right ) +x\ln \left ( 1+i{{\rm e}^{ix}} \right ) \right ) \sqrt {-{\frac {{{\rm e}^{4\,ix}}}{ \left ( {{\rm e}^{4\,ix}}-1 \right ) ^{2}}}}-{\it \_C1}/16 \right ) \sqrt { \left ( \cot \left ( 2\,x \right ) \right ) ^{2}+1} \right \} \] Mathematica raw input
DSolve[y'[x] == 4*x*Csc[x]*Sec[x]^2 - 2*Cot[2*x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> Csc[x]*(C[1] + 4*x*Log[1 - I*E^(I*x)] - 4*x*Log[1 + I*E^(I*x)] + (4*I)*PolyLog[2, (-I)*E^(I*x)] - (4*I)*PolyLog[2, I*E^(I*x)])*Sec[x]}}
Maple raw input
dsolve(diff(y(x),x) = 4*csc(x)*x*sec(x)^2-2*y(x)*cot(2*x), y(x),'implicit')
Maple raw output
y(x) = -16*(sin(2*x)*(I*dilog(1-I*exp(I*x))-I*dilog(1+I*exp(I*x))-x*ln(1-I*exp(I*x))+x*ln(1+I*exp(I*x)))*(-exp(4*I*x)/(exp(4*I*x)-1)^2)^(1/2)-1/16*_C1)*(cot(2*x)^2+1)^(1/2)