We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as = -₁x 2₂x2₂y 224 (which is discussed here) can be solved with no knowledge other than how to solve a single linear first order equation. Find a solution of the above system subject to the initial conditions x(0) = xy(0) = 0, z(0) = 0. (Assume that A₁ A₂.) x(t) = y(t) = z(t) =
We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as = -₁x 2₂x2₂y 224 (which is discussed here) can be solved with no knowledge other than how to solve a single linear first order equation. Find a solution of the above system subject to the initial conditions x(0) = xy(0) = 0, z(0) = 0. (Assume that A₁ A₂.) x(t) = y(t) = z(t) =
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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3.3-1
Transcribed Image Text:We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as
dx
dt
y(t) =
dt
dz
z(t) =
= -2₁x
-= 2₂y
(which is discussed here) can be solved with no knowledge other than how to solve a single linear first order equation. Find a solution of the above system subject to the initial conditions x(0) = x, y(0) = 0, z(0) = 0. (Assume that λ₁ # ^₂.)
x(t) =
= 2₁x-^₂y
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3.3 - 1-1
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Transcribed Image Text:We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as
dx
dt
y(t) =
dt
dz
z(t) =
= -2₁x
· = 2₂y
(which is discussed here) can be solved with no knowledge other than how to solve a single linear first order equation. Find a solution of the above system subject to the initial conditions x(0) = x, y(0) = 0, z(0) = 0. (Assume that λ₁ # ^₂.)
x(t) =
= 2₁x-^₂y
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