4.1.12 \(y'(x)=y(x) \cos (x)+\sin (x) \cos (x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0227268 (sec), leaf count = 18

\[\left \{\left \{y(x)\to c_1 e^{\sin (x)}-\sin (x)-1\right \}\right \}\]

Maple
cpu = 0.021 (sec), leaf count = 15

\[ \left \{ y \relax (x ) =-\sin \relax (x ) -1+{{\rm e}^{\sin \relax (x ) }}{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -1 + E^Sin[x]*C[1] - Sin[x]}}

Maple raw input

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

Maple raw output

y(x) = -sin(x)-1+exp(sin(x))*_C1