Consider the differential equation y" - 9y' +18 y = e³t (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = 6,3 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Σ e^(6t) Y2 (t) (c) Find a particular solution yp of the differential equation above. Yp(t): = Σ e^(3t) M M
Consider the differential equation y" - 9y' +18 y = e³t (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = 6,3 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Σ e^(6t) Y2 (t) (c) Find a particular solution yp of the differential equation above. Yp(t): = Σ e^(3t) 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
y" - 9y' +18 y = e³t.
(a) Find r₁, 2, roots of the characteristic polynomial of the equation above.
T1, T2 = 6,3
(b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above.
y₁ (t) = e^(6t)
y₂(t) =
e^(3t)
M
(c) Find a particular solution yp of the differential equation above.
Yp(t) =
M
M
M
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