ODE
\[ y''(x)+2 \cot (x) y'(x)+3 y(x)=e^x \csc (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.213338 (sec), leaf count = 56
\[\left \{\left \{y(x)\to \frac {e^{-i x} \left (4 i e^{(1+2 i) x}+5 c_2 e^{4 i x}+20 i c_1\right )}{10 \left (-1+e^{2 i x}\right )}\right \}\right \}\]
Maple ✓
cpu = 2.037 (sec), leaf count = 33
\[\left [y \left (x \right ) = \frac {\sin \left (2 x \right ) \textit {\_C2}}{\sin \left (x \right )}+\frac {\cos \left (2 x \right ) \textit {\_C1}}{\sin \left (x \right )}+\frac {{\mathrm e}^{x}}{5 \sin \left (x \right )}\right ]\] Mathematica raw input
DSolve[3*y[x] + 2*Cot[x]*y'[x] + y''[x] == E^x*Csc[x],y[x],x]
Mathematica raw output
{{y[x] -> ((4*I)*E^((1 + 2*I)*x) + (20*I)*C[1] + 5*E^((4*I)*x)*C[2])/(10*E^(I*x)*(-1 + E^((2*I)*x)))}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*cot(x)*diff(y(x),x)+3*y(x) = exp(x)*csc(x), y(x))
Maple raw output
[y(x) = 1/sin(x)*sin(2*x)*_C2+1/sin(x)*cos(2*x)*_C1+1/5*exp(x)/sin(x)]