Please explain how they get y_p(t) = Be^-t and everything after that. just dont understand the theory behind it.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please explain how they get y_p(t) = Be^-t and everything after that. just dont understand the theory behind it. thanks
 
2.41.
-t
ylo)= Y.
Y,t) = A, sint tA, cost
ý le) A, cost - Ag sint
Y,(4) = BeT
, (t) e Be'
Substitating in the diff. eq.
2 Bēt
y (t) =
+ A,sint + A, cost
N yl0) = Yo
%3D
-t
Transcribed Image Text:2.41. -t ylo)= Y. Y,t) = A, sint tA, cost ý le) A, cost - Ag sint Y,(4) = BeT , (t) e Be' Substitating in the diff. eq. 2 Bēt y (t) = + A,sint + A, cost N yl0) = Yo %3D -t
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