Consider the initial value problem x"-2x + x = -25 sin (2t); x(0)=0, x'(0)=0 (a) The characteristic equation is given by OA2-2r+1=0 OB. 2-2r+1= -25 OC. ²+r-2=0 OD. +r-2=-25 OE. None of the given answers is correct (b) The general solution of the associated homogeneous equation is OA x(t)=C₁ e 2¹ sin (2t) + C₂e-2 cos (2t) OB. x(t)=C₁e¹ sin (2t) + C₂e¹ cos (21) OC. X(t)=C₁e¹+C₂e-²1 OD. X(t)=C₁e¹+C₂te² OE. None of the given answers is correct (c) A particular solution of the differential equation is O A xp (t) = 3 sin (2t) - 4 cos (2t) OB. xp (t) = -25e¹ sin (2t) OC. xp (t)=25e¹ cos (2t) OD. xp (t)=4 sin (2t) - 3 cos (2t) OE. None of the given answers is correct d) The solution of the initial value problem is A x(t) = -3 cos (21) + 4 sin (21) +² +2p=2t
Consider the initial value problem x"-2x + x = -25 sin (2t); x(0)=0, x'(0)=0 (a) The characteristic equation is given by OA2-2r+1=0 OB. 2-2r+1= -25 OC. ²+r-2=0 OD. +r-2=-25 OE. None of the given answers is correct (b) The general solution of the associated homogeneous equation is OA x(t)=C₁ e 2¹ sin (2t) + C₂e-2 cos (2t) OB. x(t)=C₁e¹ sin (2t) + C₂e¹ cos (21) OC. X(t)=C₁e¹+C₂e-²1 OD. X(t)=C₁e¹+C₂te² OE. None of the given answers is correct (c) A particular solution of the differential equation is O A xp (t) = 3 sin (2t) - 4 cos (2t) OB. xp (t) = -25e¹ sin (2t) OC. xp (t)=25e¹ cos (2t) OD. xp (t)=4 sin (2t) - 3 cos (2t) OE. None of the given answers is correct d) The solution of the initial value problem is A x(t) = -3 cos (21) + 4 sin (21) +² +2p=2t
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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3please show written work A and B
Transcribed Image Text:Consider the initial value problem
x"-2x + x = -25 sin (2t); x(0)=0, x'(0)=0
(a) The characteristic equation is given by
OA2-2r+1=0
OB. 2-2r+1= -25
OC. ²2+r-2=0
OD. +r-2=-25
OE. None of the given answers is correct
(b) The general solution of the associated homogeneous equation is
О А. X(t)=C₁e 21,
e-21 sin (21) + C₂e-2t cos (21)
OB. x(t)=C₁e¹ sin (2t) + C₂e¹ cos (21)
OC. X(t)=C₁e¹+C₂e-21
OD. X(t)=C₁e¹+C₂te¹
OE. None of the given answers is correct
(c) A particular solution of the differential equation is
O A xp (t) = 3 sin (2t) - 4 cos (2t)
OB. xp (t) = -25e¹ sin (2t)
OC. xp (t)=25e¹ cos (2t)
OD. xp (t) = 4 sin (2t) - 3 cos (2t)
OE. None of the given answers is correct
d) The solution of the initial value problem is
OA. x(t)= -3 cos (21) + 4 sin (21) + ¹ + 2p-2t
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