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Solve the following differential equation initially at rest: d²y(t) dy(t) dt² Let x (t) = 3 u(t). +3. · + 2 y(t) = x(t) dt

Solve the following differential equation initially at rest: d²y(t) dy(t) dt² Let x (t) = 3 u(t). +3. · + 2 y(t) = x(t) dt

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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Solve the following differential equation initially at rest: d²y(t) dy(t) dt² Let x (t) = 3 u(t). +3. · + 2 y(t) = x(t) dt
Transcribed Image Text:Solve the following differential equation initially at rest: d²y(t) dy(t) dt² Let x (t) = 3 u(t). +3. · + 2 y(t) = x(t) dt
In general an Nth-order linear constant coefficient differential equation has the form dk x (t) dk yn (t) dtk dtk k=0 ak = + 2yn (t) = 0 M Σ k=0 bk homogeneous solution dyn (t) dt Complete solution: y(t) = yn (t) + yp(t) (1) particular solution dyp(t) dt +2yp (t) = x(t)
Transcribed Image Text:In general an Nth-order linear constant coefficient differential equation has the form dk x (t) dk yn (t) dtk dtk k=0 ak = + 2yn (t) = 0 M Σ k=0 bk homogeneous solution dyn (t) dt Complete solution: y(t) = yn (t) + yp(t) (1) particular solution dyp(t) dt +2yp (t) = x(t)
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