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his is some (a) Use this

his is some (a) Use this

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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This is sometimes called the Heaviside expansion theorem. (a) Use this theorem to write the solution of y" + 3y' + 2y = f(t), y(0) =y'(0)=0. (b) Give an explicit evaluation of the solution in (a) for the cases f(t) = e3t and f(t) = t. (c) Find the solutions in (b) by using the superposition principle (13).
Transcribed Image Text:This is sometimes called the Heaviside expansion theorem. (a) Use this theorem to write the solution of y" + 3y' + 2y = f(t), y(0) =y'(0)=0. (b) Give an explicit evaluation of the solution in (a) for the cases f(t) = e3t and f(t) = t. (c) Find the solutions in (b) by using the superposition principle (13).
5. When the polynomial z(p) has distinct real zeros a and b, so that 1 1 A B 2(p) (р-а)(р-b) р-а р-b for suitable constants A and B, then h(t) = Aeat + Bebt and (15) takes the form y(t) = [f(t)[Aec-1) + Bebl-=")]dt. %3D
Transcribed Image Text:5. When the polynomial z(p) has distinct real zeros a and b, so that 1 1 A B 2(p) (р-а)(р-b) р-а р-b for suitable constants A and B, then h(t) = Aeat + Bebt and (15) takes the form y(t) = [f(t)[Aec-1) + Bebl-=")]dt. %3D
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