ODE
\[ y'(x)=1-y(x) \cot (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.159999 (sec), leaf count = 15
\[\{\{y(x)\to -\cot (x)+c_1 \csc (x)\}\}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {-\cos \left (x \right )+\textit {\_C1}}{\sin \left (x \right )}\right ]\] Mathematica raw input
DSolve[y'[x] == 1 - Cot[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -Cot[x] + C[1]*Csc[x]}}
Maple raw input
dsolve(diff(y(x),x) = 1-y(x)*cot(x), y(x))
Maple raw output
[y(x) = (-cos(x)+_C1)/sin(x)]