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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#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 (*).
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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