Answer:
Therefore the complete primitive is
Therefore the general solution is
Step-by-step explanation:
Given Differential equation is
<h3>
Method of variation of parameters:</h3>
Let be a trial solution.
and
Then the auxiliary equation is
∴The complementary function is
To find P.I
First we show that and are linearly independent solution.
Let and
The Wronskian of and is
≠ 0
∴ and are linearly independent.
Let the particular solution is
Then,
Choose and such that
.......(1)
So that
Now
.......(2)
Solving (1) and (2) we get
and
Hence
and
Therefore
Therefore the complete primitive is
<h3>
Undermined coefficients:</h3>
∴The complementary function is
The particular solution is
Then,
and
Therefore the general solution is