AMath350.W13.A4.Sol

# What is8 25 0 behaviour 2 4 100p price 3 auxiliary

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Unformatted text preview: ary equation: is 0, ﬁnd pp= )dD dS+= thedp =25p +4100 = or of the= 84 ±+i. p = 100. long-termt + 25 48 t Corresponding dtp ? dt e somet), e sin(3t). diﬀerent 2 solutions: cos(3 solutions for dt2 on dt dt values of p . dt this depend 0 Sketch 0 These are linearly independent on IR by Proposition 3.37 in Course Notes. (b) Associated homogeneous equation: p00 + 8p0 + 25pp=(t) = c e 4t cos(3t) + c e 4t sin(3t). 0. General solution of associated homogeneous DE: h 64 11 2 Auxiliary equation: 2 + 8 + (t) = 0 ) ) =p (t8+=2 K . 00 = 4 ± 3i. RHS of inhomogeneous DE: F 25 = 100 p) 4t Corresponding solutions: e 4t25p =t100 )sin(3t). Substituting into DE yields: cos(3 ), e p = 4. These are linearly independent on IR by p(t) = c1 e 4t 3.37 in) Course4t sin(3t) + 4. General solution of inhomogeneous DE: Proposition cos(3t + c2 e Notes. General solution of associated homogeneous = ( ph (t) =2c1 e 44tcos(3tt) +3c2 e 4t 2 )e 4t). p0 (t) DE: 4c1 +3c )e t cos(3) ( c1 +4c sin(3 sin(3t). RHS ofICs: p(0) = p0 ) c1 F (4)= p100 ) =...
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## This document was uploaded on 02/09/2014.

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