4.1.14 \(y'(x)=y(x) \cot (x)\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0151464 (sec), leaf count = 10

\[\left \{\left \{y(x)\to c_1 \sin (x)\right \}\right \}\]

Maple
cpu = 0.025 (sec), leaf count = 8

\[ \left \{ y \relax (x ) ={\it \_C1}\,\sin \relax (x ) \right \} \] Mathematica raw input

DSolve[y'[x] == Cot[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Sin[x]}}

Maple raw input

dsolve(diff(y(x),x) = y(x)*cot(x), y(x),'implicit')

Maple raw output

y(x) = _C1*sin(x)