Category:Complementary Functions

This category contains results about Complementary Functions.
Definitions specific to this category can be found in Definitions/Complementary Functions.

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:

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