ODE
\[ y'(x)=a+b e^{k x}+c y(x) \] ODE Classification
[[_linear, `class A`]]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.221292 (sec), leaf count = 47
\[\left \{\left \{y(x)\to \frac {a (k-c)-b c e^{k x}+c c_1 (c-k) e^{c x}}{c (c-k)}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {b \,{\mathrm e}^{-x \left (c -k \right )+c x}}{-c +k}-\frac {a}{c}+{\mathrm e}^{c x} \textit {\_C1}\right ]\] Mathematica raw input
DSolve[y'[x] == a + b*E^(k*x) + c*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-(b*c*E^(k*x)) + a*(-c + k) + c*E^(c*x)*(c - k)*C[1])/(c*(c - k))}}
Maple raw input
dsolve(diff(y(x),x) = a+b*exp(k*x)+c*y(x), y(x))
Maple raw output
[y(x) = 1/(-c+k)*b*exp(-x*(c-k)+c*x)-1/c*a+exp(c*x)*_C1]