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 = 0.197788 (sec), leaf count = 15
\[\{\{y(x)\to c_1 (\cos (x)-\sin (x))\}\}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 13
\[[y \left (x \right ) = \textit {\_C1} \left (\cos \left (x \right )-\sin \left (x \right )\right )]\] 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))
Maple raw output
[y(x) = _C1*(cos(x)-sin(x))]