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Section 3.5 3.25. Find the responses of systems described by the following differential equations with the initial conditions given. For each case, show that the response satisfies the differen- tial equation and the initial conditions: dy(1) (i) +3y(t)=3(1), y(0) = -1 dt dy(1) (ii) == +3y(1) 3eu(1), y(0) = 2 dr dy(1) +10y(t) = u(t), y(0) = 2 dt d²y(1) dy(t) dy(1) (iv) +6- +5y(t) = dr² 10u(t), y(0) -1,- = = 0 dt dt 1-0 (v) -7y (vi)-10 dy(1) y(t) + y(t)=3e, y(0) = −1 +10y(1) = 20 cos (1)u(t), y(0) = -10 dt dy(1) dy(t) dy (vii) + di² di +2y(1) = 3u(1), y(0) 2 =1 dt

Section 3.5 3.25. Find the responses of systems described by the following differential equations with the initial conditions given. For each case, show that the response satisfies the differen- tial equation and the initial conditions: dy(1) (i) +3y(t)=3(1), y(0) = -1 dt dy(1) (ii) == +3y(1) 3eu(1), y(0) = 2 dr dy(1) +10y(t) = u(t), y(0) = 2 dt d²y(1) dy(t) dy(1) (iv) +6- +5y(t) = dr² 10u(t), y(0) -1,- = = 0 dt dt 1-0 (v) -7y (vi)-10 dy(1) y(t) + y(t)=3e, y(0) = −1 +10y(1) = 20 cos (1)u(t), y(0) = -10 dt dy(1) dy(t) dy (vii) + di² di +2y(1) = 3u(1), y(0) 2 =1 dt

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Section 3.5 3.25. Find the responses of systems described by the following differential equations with the initial conditions given. For each case, show that the response satisfies the differen- tial equation and the initial conditions: dy(1) (i) +3y(t)=3(1), y(0) = -1 dt dy(1) (ii) == +3y(1) 3eu(1), y(0) = 2 dr dy(1) +10y(t) = u(t), y(0) = 2 dt d²y(1) dy(t) dy(1) (iv) +6- +5y(t) = dr² 10u(t), y(0) -1,- = = 0 dt dt 1-0 (v) -7y (vi)-10 dy(1) y(t) + y(t)=3e, y(0) = −1 +10y(1) = 20 cos (1)u(t), y(0) = -10 dt dy(1) dy(t) dy (vii) + di² di +2y(1) = 3u(1), y(0) 2 =1 dt
Transcribed Image Text:Section 3.5 3.25. Find the responses of systems described by the following differential equations with the initial conditions given. For each case, show that the response satisfies the differen- tial equation and the initial conditions: dy(1) (i) +3y(t)=3(1), y(0) = -1 dt dy(1) (ii) == +3y(1) 3eu(1), y(0) = 2 dr dy(1) +10y(t) = u(t), y(0) = 2 dt d²y(1) dy(t) dy(1) (iv) +6- +5y(t) = dr² 10u(t), y(0) -1,- = = 0 dt dt 1-0 (v) -7y (vi)-10 dy(1) y(t) + y(t)=3e, y(0) = −1 +10y(1) = 20 cos (1)u(t), y(0) = -10 dt dy(1) dy(t) dy (vii) + di² di +2y(1) = 3u(1), y(0) 2 =1 dt
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