4.1.20 \(y'(x)+2 y(x) \cot (x)+\csc (x)=0\)

ODE
\[ y'(x)+2 y(x) \cot (x)+\csc (x)=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0147157 (sec), leaf count = 15

\[\left \{\left \{y(x)\to \csc ^2(x) \left (c_1+\cos (x)\right )\right \}\right \}\]

Maple
cpu = 0.029 (sec), leaf count = 21

\[ \left \{ y \relax (x ) ={\frac {-2\,\cos \relax (x ) -2\,{\it \_C1}}{-1+\cos \left (2\,x \right ) }} \right \} \] 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),'implicit')

Maple raw output

y(x) = (-2*cos(x)-2*_C1)/(-1+cos(2*x))