mronjo7n
2021-11-22
a) Through examination, identify a specific answer to
b) Investigate and identify a specific answer to
с) Track down a precise answer to
d) Track down a precise answer to
oces3y
Beginner2021-11-23Added 21 answers
Ched1950
Beginner2021-11-24Added 21 answers
Step 1
The simplest method for finding a particular solution is to try a solution of the same form as the right hand side of the nonhomogeneous equation, i.e. if it's a polynomial of degree n, we try a general polynomial of degree n and see if we can match the coefficients.
Since, the right hand side of the given equation is a constant, let us consider the constant function
Hence, by inspection,
b) Now, for this exercise, since, the right hand side of the given equation is a polynomial of degree one, let us consider the function
Substituting these in the equation gives
Hence, by inspection,
Step 2
c) From part (a), we saw that
and from part (b),
Therefore, it follows from (13) of Theorem 4.1.7 that the solution of
is the superposition of
d) Similarly, the given equation can be written as
From part (a), we saw that
and from part (b)
Therefore, it follows from (13) of Theorem 4.1.7 that the solution of
is the superposition of
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