ODE
\[ y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0266965 (sec), leaf count = 15
\[\left \{\left \{y(x)\to c_1 (\cos (x)-\sin (x))\right \}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 13
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( -\cos \left ( x \right ) +\sin \left ( x \right ) \right ) \right \} \] Mathematica raw input
DSolve[(Cos[x] + Sin[x])*y[x] + (Cos[x] - Sin[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(Cos[x] - Sin[x])}}
Maple raw input
dsolve((cos(x)-sin(x))*diff(y(x),x)+y(x)*(cos(x)+sin(x)) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(-cos(x)+sin(x))