Consider the differential equation у" - 7у + 10 у %3D — 4е e-2t (a) Find r1, r2, roots of the characteristic polynomial of the equation above. r1, r2 = 5, 2 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) : e^(5t) Σ Y2(t) : e^(2t) Σ (c) Find a particular solution y, of the differential equation above. Yp(t) = | (-1/7)e^^(-2t) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = = 4, y'(0) = 3. y(t) = -(330/84)e^(5t) + (939/84)e^(2t) - (1/7)e^(-2t) Σ
Consider the differential equation у" - 7у + 10 у %3D — 4е e-2t (a) Find r1, r2, roots of the characteristic polynomial of the equation above. r1, r2 = 5, 2 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) : e^(5t) Σ Y2(t) : e^(2t) Σ (c) Find a particular solution y, of the differential equation above. Yp(t) = | (-1/7)e^^(-2t) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = = 4, y'(0) = 3. y(t) = -(330/84)e^(5t) + (939/84)e^(2t) - (1/7)e^(-2t) Σ
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" – 7 y' + 10 y = -4e-24.
(a) Find r1, r2, roots of the characteristic polynomial of the equation above.
r1, r2 =
5, 2
Σ
(b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above.
Y1 (t)
e^(5t)
Σ
Y2(t)
e^(2t)
Σ
(c) Find a particular solution y, of the differential equation above.
Yp(t) =
(-1/7)e^(-2t)
Σ
(d) Find the solution y of the the differential equation above that satisfies the initial conditions
y(0) = 4,
y' (0) = 3.
y(t) :
-(330/84)e^(5t) + (939/84)e^(2t) - (1/7)e^(-2t)
Σ
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