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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff860867d-5eea-40c2-985f-7e9a6b60d145%2F2989a320-0c8e-42d4-b0a6-b40411edcd5b%2F4d71j88_processed.png&w=3840&q=75)
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
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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