ODE
\[ y'(x)+2 y(x) \cot (x)+\csc (x)=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.156306 (sec), leaf count = 15
\[\left \{\left \{y(x)\to \csc ^2(x) (\cos (x)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {-2 \cos \left (x \right )-2 \textit {\_C1}}{-1+\cos \left (2 x \right )}\right ]\] Mathematica raw input
DSolve[Csc[x] + 2*Cot[x]*y[x] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + Cos[x])*Csc[x]^2}}
Maple raw input
dsolve(diff(y(x),x)+csc(x)+2*y(x)*cot(x) = 0, y(x))
Maple raw output
[y(x) = (-2*cos(x)-2*_C1)/(-1+cos(2*x))]