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Consider the system of differential equations x₁ = 9/2x₁ +1/2x2 x2 = -5/2x1 + 7/2x2 Our goal is first to find the general solution of this system and then a particular solution. In all your answers below, use the scientific calculator notation. For instance 3 + 5i is written 3 + 5*i and 5te-3t is written 5*t*e^(-3*t).

Consider the system of differential equations x₁ = 9/2x₁ +1/2x2 x2 = -5/2x1 + 7/2x2 Our goal is first to find the general solution of this system and then a particular solution. In all your answers below, use the scientific calculator notation. For instance 3 + 5i is written 3 + 5*i and 5te-3t is written 5*t*e^(-3*t).

Advanced Engineering Mathematics
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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please answer parts c and d

c) The general solution of the system of differential equations is of the form X = C₁ X₁ + c₂ X 2, where C1 and | c₂ are constants, and X₁ and X₂ are the real and imaginary parts of a complex solution. [X1 X₂] = = ab sin (a) [(4x) ə əx f ・(-co 5.0 (4.x) —cosx+2 • sinx inx) •COSX ∞ d) Find the solution if the initial condition is Answer: X(t) = (21 (1)) = a Ω e (4x) ·(-2 (4-1) Pi [X₁ X₂] denotes a matrix with columns X₁ and X₂ respectively. x1 (2¹) = (-1) ² - x2 5.e −2 • cosx – sinx at t = 0. sinx
Transcribed Image Text:c) The general solution of the system of differential equations is of the form X = C₁ X₁ + c₂ X 2, where C1 and | c₂ are constants, and X₁ and X₂ are the real and imaginary parts of a complex solution. [X1 X₂] = = ab sin (a) [(4x) ə əx f ・(-co 5.0 (4.x) —cosx+2 • sinx inx) •COSX ∞ d) Find the solution if the initial condition is Answer: X(t) = (21 (1)) = a Ω e (4x) ·(-2 (4-1) Pi [X₁ X₂] denotes a matrix with columns X₁ and X₂ respectively. x1 (2¹) = (-1) ² - x2 5.e −2 • cosx – sinx at t = 0. sinx
Consider the system of differential equations x₁ = 9/2x1 +1/2x2 x2 = -5/2x1 +7/2x2 Our goal is first to find the general solution of this system and then a particular solution. In all your answers below, use the scientific calculator notation. For instance 3 + 5i is written 3 + 5*i and 5te-3t is written 5*t*e^(-3*t).
Transcribed Image Text:Consider the system of differential equations x₁ = 9/2x1 +1/2x2 x2 = -5/2x1 +7/2x2 Our goal is first to find the general solution of this system and then a particular solution. In all your answers below, use the scientific calculator notation. For instance 3 + 5i is written 3 + 5*i and 5te-3t is written 5*t*e^(-3*t).
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