\begin{definition}[Definition:Linear Combination of Solutions to Homogeneous Linear 2nd Order ODE]
Let $C_1$ and $C_2$ be real numbers.
Let $\map {y_1} x$ and $\map {y_2} x$ be particular solutions to the homogeneous linear second order ODE:
:$(1): \quad \dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = 0$
Then:
:$C_1 \, \map {y_1} x + C_2 \, \map {y_2} x$
is known as a '''linear combination of particular solutions to $(1)$.
\end{definition}