Onsider the differential equation -2e2t t4 (a) Find ₁, 2, roots of the characteristic polynomial of the equation above. T1, T2 = 2,2 Y₂ (t) = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) exp(2t) = y" - 4y + 4y texp(2t) (c) Find a particular solution yp of the differential equation above. yp (t)= te^(2t)+In(t^-2)e^(2t)-e^(2t) t> 0. Σ M M M
Onsider the differential equation -2e2t t4 (a) Find ₁, 2, roots of the characteristic polynomial of the equation above. T1, T2 = 2,2 Y₂ (t) = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) exp(2t) = y" - 4y + 4y texp(2t) (c) Find a particular solution yp of the differential equation above. yp (t)= te^(2t)+In(t^-2)e^(2t)-e^(2t) t> 0. Σ M M M
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 differential equation
-2e2t
t4
(a) Find ₁, ₂, roots of the characteristic polynomial of the equation above.
T1, T2 = 2,2
texp(2t)
y" - 4y + 4y =
te^(2t)+In(t^-2)e^(2t)-e^(2t)
t> 0.
(b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above.
y₁ (t) = exp(2t)
y₂ (t) =
(c) Find a particular solution yp of the differential equation above.
Yp (t) =
M
M
M
M
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