B part ii Consider the initial value problem (IVP) given byy" – 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 thechoice for this form.(ii) Use Green's function to solve the IVP associated to y,h (1).

Let y1(x) and y2(x) be the homogeneous solution of the initial value problem y''+pxy'+qxy=fx, yx0=y0…

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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