Let L(y) = any)(x) + an−1(n−1)(x) ++ a₁y′(x) + ao y(x) where a0, a1, .,a,, are fixed constants. Consider the nth order linear differential equation L(y) = 2ex cos x + xe⁹x => Suppose that it is known that L[v1(x)] = 4xe⁹x L[y2(x)] = 5e⁹x sinx = when y(x) 40xe9x when y2(x) = 35e⁹x cos x L[v3(x)]=3ex cos x when y3(x) = 9ex cos x + 18ex sin.x Find a particular solution to (*).
Let L(y) = any)(x) + an−1(n−1)(x) ++ a₁y′(x) + ao y(x) where a0, a1, .,a,, are fixed constants. Consider the nth order linear differential equation L(y) = 2ex cos x + xe⁹x => Suppose that it is known that L[v1(x)] = 4xe⁹x L[y2(x)] = 5e⁹x sinx = when y(x) 40xe9x when y2(x) = 35e⁹x cos x L[v3(x)]=3ex cos x when y3(x) = 9ex cos x + 18ex sin.x Find a particular solution to (*).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![#2: Let
L(y) =
any()(x) + an-1(n-1)(x) ++ a₁y'(x) + ao y(x)
where a0, a1,
L(y)
,...,a,, are fixed constants. Consider the nth order linear differential equation
2e⁹x cos x + xe⁹x
Suppose that it is known that
L[v1(x)] = 4xe⁹x
when y(x)
=
40xe9x
L[y2(x)] =
5ex sinx
when y2(x) = 35e⁹x cos x
L[y3(x)] = 3x cos x
when y3(x) = 9ex cos x + 18e⁹x sinx
Find a particular solution to (*).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8a9802b-ded9-4a7b-93c8-71218002814a%2F0adfb23b-fef4-4958-bb60-6dc9dd9928ec%2Fzsckilq_processed.png&w=3840&q=75)
Transcribed Image Text:#2: Let
L(y) =
any()(x) + an-1(n-1)(x) ++ a₁y'(x) + ao y(x)
where a0, a1,
L(y)
,...,a,, are fixed constants. Consider the nth order linear differential equation
2e⁹x cos x + xe⁹x
Suppose that it is known that
L[v1(x)] = 4xe⁹x
when y(x)
=
40xe9x
L[y2(x)] =
5ex sinx
when y2(x) = 35e⁹x cos x
L[y3(x)] = 3x cos x
when y3(x) = 9ex cos x + 18e⁹x sinx
Find a particular solution to (*).
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