4.1.13 \(y'(x)=y(x) \cos (x)+e^{\sin (x)}\)

ODE
\[ y'(x)=y(x) \cos (x)+e^{\sin (x)} \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.025223 (sec), leaf count = 14

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

Maple
cpu = 0.005 (sec), leaf count = 11

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

DSolve[y'[x] == E^Sin[x] + Cos[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> E^Sin[x]*(x + C[1])}}

Maple raw input

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

Maple raw output

y(x) = (x+_C1)*exp(sin(x))