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

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

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (-\cos \relax (x ) +\sin \relax (x ) \right ) \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*(-cos(x)+sin(x))