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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) =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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3.3-1

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
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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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
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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