23. For the differential equation y"+y = 3 sin(2t) +t cos(2t) the form of the particular solution is a) Acos(2t) + Bsin(2t) + Ccos(2t) + Dsin(2t) b) Asin(2t) + Ctcos(2t) c) (At + B)cos(2t) + (Ct + D)sin(2t) d) Acos(2t) + Ctsin(2t) 24. Given the differential equation y" +y' 0 and the solutions y, the wronskian 1, y2 = cost and y, = sint determine %3D a) cos?t-sin?t c) sin?t - cos?t b) 0 d) 1
23. For the differential equation y"+y = 3 sin(2t) +t cos(2t) the form of the particular solution is a) Acos(2t) + Bsin(2t) + Ccos(2t) + Dsin(2t) b) Asin(2t) + Ctcos(2t) c) (At + B)cos(2t) + (Ct + D)sin(2t) d) Acos(2t) + Ctsin(2t) 24. Given the differential equation y" +y' 0 and the solutions y, the wronskian 1, y2 = cost and y, = sint determine %3D a) cos?t-sin?t c) sin?t - cos?t b) 0 d) 1
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
Q23,24
Transcribed Image Text:22. For the differential equation
y" +3y'-4y = 3cosx + 5sin(4x) the form of the
particular solution is
a) Acosx + Bsinx + x(Ccos(4x) + Dsin(4x))
b) Acosx + Bsinx + Ccos(4x) + Dsin(4x)
c) Acosx + Bsinx + Cx sin(4x)
d) Acosx + Bsin(4x)
23. For the differential equation
y" +y = 3 sin(2t) +t cos(2t) the form of the particular
solution is
a) Acos(2t) + Bsin(2t) + Ccos(2t) + Dsin(2t)
b) Asin(2t) + Ctcos(2t)
c) (At + B)cos(2t) + (Ct +D)sin(2t)
d) Acos(2t) + Ctsin(2t)
24. Given the differential equation y" +y' = 0 and the
solutions y, =1, y2 = cost and y, = sint determine
the wronskian
%3D
!!
a) cos?t - sin²t
c) sin?t - cos?t
b) 0
d) 1
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