4.1.17 \(y'(x)=y(x) (\cot (x)+2 \csc (2 x))\)

ODE
\[ y'(x)=y(x) (\cot (x)+2 \csc (2 x)) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0285719 (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 = 0.14 (sec), leaf count = 39

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}\,\cot \relax (x ) \left (\cos \relax (x ) -\cos \left (3\,x \right ) \right ) }{ \left (\cot \relax (x ) \right ) ^{2}\sin \left (2\,x \right ) +2\,\cot \relax (x ) -\sin \left (2\,x \right ) }} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*cot(x)*(cos(x)-cos(3*x))/(cot(x)^2*sin(2*x)+2*cot(x)-sin(2*x))