Consider the differential equation y' (t) + 8y(t) = 6cos(lt)u(t), with initial condition y(0) = 6, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) (12s^2+48s+6)/((s+8)(s^2+1)) help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form , where c is a constant and the s-p root p is a constant. Both c and p may be complex. Y(s) = 342/65(1/(s+8)) + 48/65"(s/(s^2+1)) + 6/65*(1/(s^2+1)) Find the inverse Laplace transform of Y(s). The solution must consist of all real terms. (Remeber to use u(t).) y(t) = L-1 {Y(s)} = | 342/65e^(-8t)+48/65cos(t)+6/65sin(t) help (formulas)
Consider the differential equation y' (t) + 8y(t) = 6cos(lt)u(t), with initial condition y(0) = 6, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) (12s^2+48s+6)/((s+8)(s^2+1)) help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form , where c is a constant and the s-p root p is a constant. Both c and p may be complex. Y(s) = 342/65(1/(s+8)) + 48/65"(s/(s^2+1)) + 6/65*(1/(s^2+1)) Find the inverse Laplace transform of Y(s). The solution must consist of all real terms. (Remeber to use u(t).) y(t) = L-1 {Y(s)} = | 342/65e^(-8t)+48/65cos(t)+6/65sin(t) help (formulas)
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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Transcribed Image Text:Consider the differential equation y' (t) + 8y(t) = 6cos(lt)u(t),
with initial condition y(0) = 6,
Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s
Y(s) = (12s^2+48s+6)/((s+8)(s^2+1))
help (formulas)
Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form , where c is a constant and the
s-p
root p is a constant. Both c and p may be complex.
Y(s) =
342/65(1/(s+8))
+ 48/65*(s/(s^2+1))
+ 6/65*(1/(s^2+1))
Find the inverse Laplace transform of Y(s). The solution must consist of all real terms. (Remeber to use u(t).)
y(t) = L-1 {Y(s)}
= 342/65e^(-8t)+48/65cos(t)+6/65sin(t)
help (formulas)
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