ODE
\[ y'(x)=a+b e^{k x}+c y(x) \] ODE Classification
[[_linear, `class A`]]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.028643 (sec), leaf count = 34
\[\left \{\left \{y(x)\to -\frac {a}{c}+\frac {b e^{k x}}{k-c}+c_1 e^{c x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =-{\frac {a}{c}}+{\frac {b{{\rm e}^{kx}}}{-c+k}}+{{\rm e}^{cx}}{\it \_C1} \right \} \] Mathematica raw input
DSolve[y'[x] == a + b*E^(k*x) + c*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(a/c) + (b*E^(k*x))/(-c + k) + E^(c*x)*C[1]}}
Maple raw input
dsolve(diff(y(x),x) = a+b*exp(k*x)+c*y(x), y(x),'implicit')
Maple raw output
y(x) = -1/c*a+1/(-c+k)*b*exp(k*x)+exp(c*x)*_C1