0 3 t Given the ODE x' – x = f(t) with initial condition x(0) = 0 and that f(t) 3 (i) Sketch the signal f(t). (ii) Use the Heaviside function to express f(t) as a one-line function. (iii) Solve for x (t) using the Laplace transform. HINT: Rearrange f(t) after using u(t – a) to be sure everything is shifted properly, so we can apply L. ..

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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0 <t < 3,
t > 3
t
Given the ODE x' – x = f(t) with initial condition x(0) = 0 and that f(t)
3
(i) Sketch the signal f(t).
(ii) Use the Heaviside function to express f(t) as a one-line function.
(iii) Solve for x (t) using the Laplace transform.
HINT: Rearrange f(t) after using u(t – a) to be sure everything is shifted properly, so we can apply L.
..
Transcribed Image Text:0 <t < 3, t > 3 t Given the ODE x' – x = f(t) with initial condition x(0) = 0 and that f(t) 3 (i) Sketch the signal f(t). (ii) Use the Heaviside function to express f(t) as a one-line function. (iii) Solve for x (t) using the Laplace transform. HINT: Rearrange f(t) after using u(t – a) to be sure everything is shifted properly, so we can apply L. ..
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