Definition:Complementary Function of Linear First Order ODE With Constant Coefficients

Definition

Consider the linear first order ODE with constant coefficients:

$(1): \quad \dfrac {\d y} {\d x} + a y = \map Q x$

The general solution to the reduced equation:

$\dfrac {\d y} {\d x} + a y = 0$

is the complementary function of $(1)$.

From First Order ODE: $\dfrac {\d y} {\d x} = k y$, the complementary function of $(1)$ is $C e^{-a x}$.

Sources

• 1958: G.E.H. Reuter: Elementary Differential Equations & Operators ... (previous) ... (next): Chapter $1$: Linear Differential Equations with Constant Coefficients: $\S 1$. The first order equation: $\S 1.3$ The form of the general solution