The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots. Which of the following is the form of the complementary function y. of the differential equation? Ye = C1em1* + C2em2* + ...+ Cnemn* Ye = eax[(c +c2x ++ cpxP-1)cos(bx) + (cp+1+ Cp+2X + +C2,XP=1)sin (bx)] ...+ Ye = Cemx + C2xemx +.. +CpxP-lemx Ye = eax[c,cos (bx) + c2sin (bx)]
The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots. Which of the following is the form of the complementary function y. of the differential equation? Ye = C1em1* + C2em2* + ...+ Cnemn* Ye = eax[(c +c2x ++ cpxP-1)cos(bx) + (cp+1+ Cp+2X + +C2,XP=1)sin (bx)] ...+ Ye = Cemx + C2xemx +.. +CpxP-lemx Ye = eax[c,cos (bx) + c2sin (bx)]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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![The auxiliary equation of a non-homogeneous differential equation has
complex and distinct roots. Which of the following is the form of the
complementary function
of the differential equation?
Ye
Ye
e = * + ..+ cnemn*
Cemix + C2em
Ye = eax[(c +c2x+ .+ ..+
+ c,xP-1)cos(bx) + (cp+1+ Cp+2x +
c2pxP-1)sin (bx)]
%3D
*+ C2p
Ye = Cemx + c2xemx +..+ C,xP-lemx
C16
Yc = eax[ccos (bx) + c2sin (bx)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9410ab1-0cec-4fd4-86d7-290a5d876af4%2F803cf1d4-f356-4432-aee9-abcce0070df9%2Ffurb15d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The auxiliary equation of a non-homogeneous differential equation has
complex and distinct roots. Which of the following is the form of the
complementary function
of the differential equation?
Ye
Ye
e = * + ..+ cnemn*
Cemix + C2em
Ye = eax[(c +c2x+ .+ ..+
+ c,xP-1)cos(bx) + (cp+1+ Cp+2x +
c2pxP-1)sin (bx)]
%3D
*+ C2p
Ye = Cemx + c2xemx +..+ C,xP-lemx
C16
Yc = eax[ccos (bx) + c2sin (bx)]
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