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a) For c, a constants, B E R define X = ect+aB, Prove that dX = (c+a?)X;dt +aXpdB. b) For c, a1,..., an constants, B = (B1(t),..., Bn(t)) e R" define %3D Xt = exp (ct + %3D j=1 Prove that AX; = (c+ E«3)Xxdt + X. adBj %3D j=1 j=1

a) For c, a constants, B E R define X = ect+aB, Prove that dX = (c+a?)X;dt +aXpdB. b) For c, a1,..., an constants, B = (B1(t),..., Bn(t)) e R" define %3D Xt = exp (ct + %3D j=1 Prove that AX; = (c+ E«3)Xxdt + X. adBj %3D j=1 j=1

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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4.6. a) For c, a constants, B ER define X = ect+aB, Prove that dX = (c+a?)X,dt +aX,dB. b) For c, a1,..., an constants, B = (B1(t),..., Bn(t)) E R" define n Xt = exp ( ct + j=1 Prove that dX1 = (c+E})X,dt + Xt( agdB; j=1 j=1
Transcribed Image Text:4.6. a) For c, a constants, B ER define X = ect+aB, Prove that dX = (c+a?)X,dt +aX,dB. b) For c, a1,..., an constants, B = (B1(t),..., Bn(t)) E R" define n Xt = exp ( ct + j=1 Prove that dX1 = (c+E})X,dt + Xt( agdB; j=1 j=1
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