4.1.36 \(y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))\)

ODE
\[ y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x))) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0148363 (sec), leaf count = 17

\[\left \{\left \{y(x)\to c_1 e^{x (a+\sin (\log (x)))}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 14

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{x \left (\sin \left (\ln \relax (x ) \right ) +a \right ) }} \right \} \] Mathematica raw input

DSolve[y'[x] == (a + Cos[Log[x]] + Sin[Log[x]])*y[x],y[x],x]

Mathematica raw output

{{y[x] -> E^(x*(a + Sin[Log[x]]))*C[1]}}

Maple raw input

dsolve(diff(y(x),x) = (a+cos(ln(x))+sin(ln(x)))*y(x), y(x),'implicit')

Maple raw output

y(x) = _C1*exp(x*(sin(ln(x))+a))