gabolzm6d
2022-04-08
Raina Blackburn
Beginner2022-04-09Added 10 answers
Step 1
The equations defined by operators of the form
, with can be solved applying the substitution . Observe that is not in normal form so you have to study the equation in
Consider
,\ if
you obtain
and
.
From these relations if follows that
The initial equation is now
, so
which is a second order differential equation with constant coefficients and the general solution is given by , where is the solution for the homogeneous problem and is the particular solution.
The characteristic polynomial associated to the homogeneous problem is , whose roots are , then
The general particular solution is , with to determine.
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