Linear Differential Equation
Differential operator
, where
differential operatorConsidering
,
Linear differential equation with constant coefficients
General solution of
.Let's factorize
. Then, we find the general solution for each factor 
and 
General solution whose total sum is
.The general solution of
is obtained by adding to the general solution of 
the singular solutions of 
Homogeneous linear differential equation
General solution
Let
. Then, we have:
Substituting these equations, we obtain
.Next, we find its general solution and introduce the transformation
.General solution of the system of linear differential equation with constant coefficients
Let's multiply the first equation by
and the second equation by 
and subtract from the respective members. Considering
, we obtain
Then, we find the general solution of
.The general solution of
is found in a similar manner.Then, the relation between the arbitrary constants
is found.[0]Top