Consider the following ODE: p(D)x = f, where p(r) is the degree 2 polynomial p(r) = d Let f(t) = et. We will assume that b, c, s are all real numbers. dt p2 + br +c and D (a) Give non-zero values for b, c and s such that xp(t) = f(t) for all t e R, where xp(t) is a particular solution of the ODE p(D)x = f. (b) Give non-zero values for b, c, s, and also give values for u, v, such that x(t) = g(t) for all t E R, where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions = u and x'(0) = %3D %3D æ(0) = v.
Consider the following ODE: p(D)x = f, where p(r) is the degree 2 polynomial p(r) = d Let f(t) = et. We will assume that b, c, s are all real numbers. dt p2 + br +c and D (a) Give non-zero values for b, c and s such that xp(t) = f(t) for all t e R, where xp(t) is a particular solution of the ODE p(D)x = f. (b) Give non-zero values for b, c, s, and also give values for u, v, such that x(t) = g(t) for all t E R, where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions = u and x'(0) = %3D %3D æ(0) = v.
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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Transcribed Image Text:Consider the following ODE: p(D)x = ƒ, where p(r) is the degree 2 polynomial p(r)
d
Let f(t) = est. We will assume that b, c, s are all real numbers.
dt
p2 + br + c and D
(a) Give non-zero values for b, c and s such that xp(t) :
particular solution of the ODE p(D)x = f.
(b) Give non-zero values for 6, c, s,
where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions
f(t) for all t E R, where xp(t) is a
and also give values for u, v, such that x(t) = g(t) for all t e R,
x(0)
= u and x' (0)
= v.
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