ODE
\[ y'(x)=a \cos (b x+c)+k y(x) \] ODE Classification
[[_linear, `class A`]]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.216082 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {a (b \sin (b x+c)-k \cos (b x+c))}{b^2+k^2}+c_1 e^{k x}\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 40
\[\left [y \left (x \right ) = {\mathrm e}^{k x} \textit {\_C1} +\frac {a \left (b \sin \left (b x +c \right )-\cos \left (b x +c \right ) k \right )}{b^{2}+k^{2}}\right ]\] Mathematica raw input
DSolve[y'[x] == a*Cos[c + b*x] + k*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^(k*x)*C[1] + (a*(-(k*Cos[c + b*x]) + b*Sin[c + b*x]))/(b^2 + k^2)}}
Maple raw input
dsolve(diff(y(x),x) = a*cos(b*x+c)+k*y(x), y(x))
Maple raw output
[y(x) = exp(k*x)*_C1+a*(b*sin(b*x+c)-cos(b*x+c)*k)/(b^2+k^2)]