ODE
\[ y'(x)=y(x) (\cot (x)+2 \csc (2 x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.177484 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {c_1 \sin ^{\frac {3}{2}}(x) \sqrt {\sin (2 x)}}{\cos ^{\frac {3}{2}}(x)}\right \}\right \}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \cot \left (x \right ) \left (\cos \left (x \right )-\cos \left (3 x \right )\right )}{\sin \left (2 x \right ) \left (\cot ^{2}\left (x \right )\right )-\sin \left (2 x \right )+2 \cot \left (x \right )}\right ]\] Mathematica raw input
DSolve[y'[x] == (Cot[x] + 2*Csc[2*x])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1]*Sin[x]^(3/2)*Sqrt[Sin[2*x]])/Cos[x]^(3/2)}}
Maple raw input
dsolve(diff(y(x),x) = (2*csc(2*x)+cot(x))*y(x), y(x))
Maple raw output
[y(x) = _C1*cot(x)*(cos(x)-cos(3*x))/(sin(2*x)*cot(x)^2-sin(2*x)+2*cot(x))]