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3) Consider the differential equation a' +x = 2H(t – 3) – H(t – 1), x(0) = 1, (3) %3D i) Show that z(t) = H (t – 1) (–1+ el-t) + 2 H (t – 3) (1 – et) + et and solution of (3) ii) Plot the graph of x(t) on the interval [0, 10]. Suggestion: Note that the function is decreasing in the interval [0,3] and increasing in the interval [3, co). Also note that x(1) = 0.367. > 0, x(3) = -0.814. < 0 and that lim+0#(t) = 1.

3) Consider the differential equation a' +x = 2H(t – 3) – H(t – 1), x(0) = 1, (3) %3D i) Show that z(t) = H (t – 1) (–1+ el-t) + 2 H (t – 3) (1 – et) + et and solution of (3) ii) Plot the graph of x(t) on the interval [0, 10]. Suggestion: Note that the function is decreasing in the interval [0,3] and increasing in the interval [3, co). Also note that x(1) = 0.367. > 0, x(3) = -0.814. < 0 and that lim+0#(t) = 1.

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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3) Consider the differential equation a' +x = 2H(t – 3) – H(t – 1), x(0) = 1, (3) %3D i) Show that r(t) = H (t – 1) (–1+e-f) + 2 H (t – 3) (1 – e³-+) + e=t and solution of (3) ii) Plot the graph of x(t) on the interval [0, 10]. Suggestion: Note that the function is decreasing in the interval [0,3] and increasing in the interval [3, co). Also note that x(1) = 0.367. > 0, x(3) = -0.814. < 0 and that lim+00#(t) = 1.
Transcribed Image Text:3) Consider the differential equation a' +x = 2H(t – 3) – H(t – 1), x(0) = 1, (3) %3D i) Show that r(t) = H (t – 1) (–1+e-f) + 2 H (t – 3) (1 – e³-+) + e=t and solution of (3) ii) Plot the graph of x(t) on the interval [0, 10]. Suggestion: Note that the function is decreasing in the interval [0,3] and increasing in the interval [3, co). Also note that x(1) = 0.367. > 0, x(3) = -0.814. < 0 and that lim+00#(t) = 1.
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