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(1) Consider the differential equation * + 4x = k(t) where k(t) = fo, 0 4. (a) Rewrite the given ODE using the Heaviside unit step func- tion. (b) If the initial conditions (0) = 1 and ż(0) = 0 are given, us- ing Laplace transform method solve the Initial Value Prob- lem.

(1) Consider the differential equation * + 4x = k(t) where k(t) = fo, 0 4. (a) Rewrite the given ODE using the Heaviside unit step func- tion. (b) If the initial conditions (0) = 1 and ż(0) = 0 are given, us- ing Laplace transform method solve the Initial Value Prob- lem.

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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(1) Consider the differential equation Ï +4r = k(t) Jo, 0<t<4; where k(t)= 3, t> 4. (a) Rewrite the given ODE using the Heaviside unit step func- tion. (b) If the initial conditions x(0) = 1 and (0) = 0 are given, us- ing Laplace transform method solve the Initial Value Prob- lem.
Transcribed Image Text:(1) Consider the differential equation Ï +4r = k(t) Jo, 0<t<4; where k(t)= 3, t> 4. (a) Rewrite the given ODE using the Heaviside unit step func- tion. (b) If the initial conditions x(0) = 1 and (0) = 0 are given, us- ing Laplace transform method solve the Initial Value Prob- lem.
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