Linear Diff erential Equations with Constant Coeffi cients 3-9
3.1.6 General Solution, Basis and Particular Solution
A general solution of a second-order linear homogeneous (L.H.)
equation
() () 0yPxyQxy++=
′′ ′
on an open interval I is of the form
11 2 2
ycy cy=+
where
1
y
and
2
y
are
linearly independent on I (they are not proportional to each other) and
1
c
and
2
c
are arbitrary constants. Then,
1
y
and
2
y
are called the basis
(fundamental system) of solution for the L.H. equation.
A particular solution of L.H. equation is obtained by giving specifi c
values to
1
c
and
2
c
in the general solution.
3.1.7 Second Order Linear Homogeneous Equations
with Constant Coeffi cients
We will now discuss the method of solution of a homogeneous linear
differential ...