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The differential equation (dynamic) model for a chemical process is as follows: d²y dy dt² dt +5 +3y: = where u(t) is the single input function of time. y(0) and dy/dt (0) are both zero. What are the functions of the time in the solution to the ODE for output y(t) for each of the following cases? be-2t (a) u(t) (b) u(t) = ct b and c are constants. 2u(t) = Note: You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).

The differential equation (dynamic) model for a chemical process is as follows: d²y dy dt² dt +5 +3y: = where u(t) is the single input function of time. y(0) and dy/dt (0) are both zero. What are the functions of the time in the solution to the ODE for output y(t) for each of the following cases? be-2t (a) u(t) (b) u(t) = ct b and c are constants. 2u(t) = Note: You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).

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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The differential equation (dynamic) model for a chemical process is as follows: d²v dy di² dt +5 + 3y = 2u(t) where u(t) is the single input function of time. y(0) and dy/dt (0) are both zero. What are the functions of the time in the solution to the ODE for output y(t) for each of the following cases? -2t (a) u(t) = be (b) u(t) = ct b and care constants. Note: You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).
Transcribed Image Text:The differential equation (dynamic) model for a chemical process is as follows: d²v dy di² dt +5 + 3y = 2u(t) where u(t) is the single input function of time. y(0) and dy/dt (0) are both zero. What are the functions of the time in the solution to the ODE for output y(t) for each of the following cases? -2t (a) u(t) = be (b) u(t) = ct b and care constants. Note: You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).
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