Consider the differential equation y" – 4y' + 3 y = -2 e". (a) Find r1, r2, roots of the characteristic polynomial of the equation above. T1,r2 1,3 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) = Σ e^t Y2(t) = e^(3t) Σ (C) Find a particular solution y, of the differential equation above. Yp(t) = | 2e^(2t) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -2, 3/ (0) = -4. %3D y(t) = 2e^(2t)-4t Σ

Consider the differential equation y" – 4y' + 3 y = -2 e". (a) Find r1, r2, roots of the characteristic polynomial of the equation above. T1,r2 1,3 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) = Σ e^t Y2(t) = e^(3t) Σ (C) Find a particular solution y, of the differential equation above. Yp(t) = | 2e^(2t) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -2, 3/ (0) = -4. %3D y(t) = 2e^(2t)-4t 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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Consider the differential equation
y" – 4y' + 3 y = -2 e2.
(a) Find r1, r2, roots of the characteristic polynomial of the equation above.
T1, 12 =
1,3
Σ
(b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above.
Y1(t) =
ent
Σ
Y2(t) =
e^(3t)
Σ
(C) Find a particular solution y, of the differential equation above.
Yp(t) = 2e^(21)
Σ
(d) Find the solution y of the the differential equation above that satisfies the initial conditions
У0) — — 2,
3/ (0) = -4.
y(t) = 2e^(2t)-4t
Σ

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