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-12e-7t u(t), Consider the differential equation y" (t) + 11y'(t) + 30y(t) with initial conditions y(0) = -13, and y' (0) = 82. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = 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 s-p where c is a constant and the root p is a constant. Both c and p may be complex. Y(s) + + Find the inverse Laplace transform of Y(s). (Remember to use u(t) or step(t). y(t) = L" {Y(s)} = help (formulas)

-12e-7t u(t), Consider the differential equation y" (t) + 11y'(t) + 30y(t) with initial conditions y(0) = -13, and y' (0) = 82. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = 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 s-p where c is a constant and the root p is a constant. Both c and p may be complex. Y(s) + + Find the inverse Laplace transform of Y(s). (Remember to use u(t) or step(t). y(t) = L" {Y(s)} = help (formulas)

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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Consider the differential equation y" (t) + 11y'(t) + 30y(t) = –12e-tu(t), with initial conditions y(0) = -13, and y' (0) = 82. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) 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 root p is a constant. Both c and p may be complex. Y(s) + + Find the inverse Laplace transform of Y(s). (Remember to use u(t) or step(t). y(t) = L1 {Y(s)} = help (formulas)
Transcribed Image Text:Consider the differential equation y" (t) + 11y'(t) + 30y(t) = –12e-tu(t), with initial conditions y(0) = -13, and y' (0) = 82. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) 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 root p is a constant. Both c and p may be complex. Y(s) + + Find the inverse Laplace transform of Y(s). (Remember to use u(t) or step(t). y(t) = L1 {Y(s)} = help (formulas)
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