Definition:Complementary Function

Definition

Consider the linear second order ODE with constant coefficients:

$(1): \quad \dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = \map R x$

where $p$ and $q$ are constants and $\map R x$ is a function of $x$.

The complementary function of $(1)$ is the general solution to the homogeneous linear second order ODE with constant coefficients:

$\dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = 0$

Also see

• Results about complementary functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complementary function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation: differential equations of the second order: $(4)$ Linear equations with constant coefficients of the form $a \dfrac {\d^2 y} {\d x^2} + b \dfrac {\d y} {\d x} + c y = \map f x$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complementary function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation: differential equations of the second order: $(4)$ Linear equations with constant coefficients of the form $a \dfrac {\d^2 y} {\d x^2} + b \dfrac {\d y} {\d x} + c y = \map f x$