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If the source function (the right hand side) of a differential equation whose characteristic equation has roots r, = 0 , r2 = 0 , rz = -1, r, = -1, rz = 2i , r, = -2i is f(x) = A + Bx + Ce-* + De²x + Ecos2x, how should its particular solution be chosen? (A, B, C, D, E, a, b, c, d, k, m are arbitrary constan ts.) A) yo = (a + bx)x + cx?e¬x + de2x + (kcos 2x + msin2x) B) y, = (a + bx)+ ce¬* + de2x + (kcos 2x + msin2x) C) y. = (a + bx)x² + ce¬x + de²x + (kcos 2x + msin2x) %3D D) y, = (a + bx)x² + cx²e¬x + de2* + (kcos 2x + msin2x) E) y. = (a + bx)x² + cx²e¬x + de²* + x(kcos 2x + msin2x)

If the source function (the right hand side) of a differential equation whose characteristic equation has roots r, = 0 , r2 = 0 , rz = -1, r, = -1, rz = 2i , r, = -2i is f(x) = A + Bx + Ce-* + De²x + Ecos2x, how should its particular solution be chosen? (A, B, C, D, E, a, b, c, d, k, m are arbitrary constan ts.) A) yo = (a + bx)x + cx?e¬x + de2x + (kcos 2x + msin2x) B) y, = (a + bx)+ ce¬* + de2x + (kcos 2x + msin2x) C) y. = (a + bx)x² + ce¬x + de²x + (kcos 2x + msin2x) %3D D) y, = (a + bx)x² + cx²e¬x + de2* + (kcos 2x + msin2x) E) y. = (a + bx)x² + cx²e¬x + de²* + x(kcos 2x + msin2x)

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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If the source function (the right hand side) of a differential equation whose characteristic equation has roots r, = 0 , r2 = 0, r3 = -1, r, = -1, r; = 2i , rg = -2i is f(x) = A+ Bx + Ce¬x + De2x + Ecos2x, how should its particular solu tion be chosen? (A, B , C, D,E, a, b, c, d,k,m are arbitrary constan ts.) A) yo = (a + bx)x + cx²e¬* + de 2* + (kcos 2x + msin2x) B) y. = (a + bx) + ce¬* + de²x + (kcos 2x + msin2x) C) y. = (a + bx)x² + ce¬x + de²x + (kcos 2x + msin2x) D) y. = (a + bx)x² + cx²e¬* + de2x + (kcos 2x + msin2x) E) y. = (a + bx)x² + cx²e¬x + de2* + x(kcos 2x + msin2x)
Transcribed Image Text:If the source function (the right hand side) of a differential equation whose characteristic equation has roots r, = 0 , r2 = 0, r3 = -1, r, = -1, r; = 2i , rg = -2i is f(x) = A+ Bx + Ce¬x + De2x + Ecos2x, how should its particular solu tion be chosen? (A, B , C, D,E, a, b, c, d,k,m are arbitrary constan ts.) A) yo = (a + bx)x + cx²e¬* + de 2* + (kcos 2x + msin2x) B) y. = (a + bx) + ce¬* + de²x + (kcos 2x + msin2x) C) y. = (a + bx)x² + ce¬x + de²x + (kcos 2x + msin2x) D) y. = (a + bx)x² + cx²e¬* + de2x + (kcos 2x + msin2x) E) y. = (a + bx)x² + cx²e¬x + de2* + x(kcos 2x + msin2x)
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