4.9.15 \((1-\sin (x)) y'(x)+y(x) \cos (x)=0\)

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

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (\sin \relax (x ) -1 \right ) \right \} \] 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)