y" + 2y' + 5y = 13e²t (a) Find a particular solution of this equation. (b) Solve the initial value problem of this equation with initial conditions y(0) = 1, y'(0) = 0.
The given differential equation is
.....................................(1)
The auxiliary equation of (1) is
Therefore the complementary function of (1) is
where and are arbitary constant .
Let the trial particular integral solution be
....................................(2)
Where A is a constant.
Then
Now we put the value of in (1) we get the value of A.
Now we put the value of A in (2) we get
Hence the particular integral is
Therefore the general solution is
...................(3)
Where and are arbitary constant .
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