ODE
\[ y''(x)+2 \cot (x) y'(x)+3 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.184616 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {c_2 e^{3 i x}}{2 \left (-1+e^{2 i x}\right )}+c_1 e^{-2 i x} \csc (x)\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \sin \left (2 x \right )}{\sin \left (x \right )}+\frac {\textit {\_C2} \cos \left (2 x \right )}{\sin \left (x \right )}\right ]\] Mathematica raw input
DSolve[3*y[x] + 2*Cot[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^((3*I)*x)*C[2])/(2*(-1 + E^((2*I)*x))) + (C[1]*Csc[x])/E^((2*I)*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*cot(x)*diff(y(x),x)+3*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/sin(x)*sin(2*x)+_C2/sin(x)*cos(2*x)]