4.1.7 \(y'(x)=a+b e^{k x}+c y(x)\)

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

\[ \left \{ y \relax (x ) =-{\frac {a}{c}}+{\frac {b{{\rm e}^{kx}}}{-c+k}}+{{\rm e}^{cx}}{\it \_C1} \right \} \] 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