ODE
\[ (1-\sin (x)) y'(x)+y(x) \cos (x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0288154 (sec), leaf count = 13
\[\left \{\left \{y(x)\to -c_1 (\sin (x)-1)\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 10
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \sin \left ( x \right ) -1 \right ) \right \} \] Mathematica raw input
DSolve[Cos[x]*y[x] + (1 - Sin[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(C[1]*(-1 + Sin[x]))}}
Maple raw input
dsolve((1-sin(x))*diff(y(x),x)+y(x)*cos(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(sin(x)-1)