Consider the initial value problem (IVP) given by y" – 4y = e ", y(1) = 1, y (1) = 0. (*) (a) Give the two IVPS of the associated homogeonous DE (yn(z)) and nonhomoge- neous DE (y„h(x)) needed to solve (*). (b) From your answers in (a), (i) Solve the IVP associated to ynh(x) using the method of undetermined coeffi- cients. Give the form of the particular solution to solve y (1) and explain the choice for this form. (ii) Use Green's function to solve the IVP associated to y,h (1).
Consider the initial value problem (IVP) given by y" – 4y = e ", y(1) = 1, y (1) = 0. (*) (a) Give the two IVPS of the associated homogeonous DE (yn(z)) and nonhomoge- neous DE (y„h(x)) needed to solve (*). (b) From your answers in (a), (i) Solve the IVP associated to ynh(x) using the method of undetermined coeffi- cients. Give the form of the particular solution to solve y (1) and explain the choice for this form. (ii) Use Green's function to solve the IVP associated to y,h (1).
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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B part ii
Transcribed Image Text:Consider the initial value problem (IVP) given by
y" – 4y = e-", y(1) = 1, y(1) = 0. (*)
(a) Give the two IVPS of the associated homogeonous DE (yn (x)) and nonhomoge-
neous DE (ynh(x)) needed to solve (*).
(b) From your answers in (a),
(i) Solve the IVP associated to ynh(z) using the method of undetermined coeffi-
cients. Give the form of the particular solution to solve ynh (x) and explain the
choice for this form.
(ii) Use Green's function to solve the IVP associated to y,h (1).
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