Consider the second order differential equation with initial conditions u" 2.5u' + 6.5u = = -7.5 sin(3t), u(1) = -5.5, u'(1) = -4. Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the "velocity function" u'. Do not use u(t) or v(t) to represent these functions. Expressions like sin(t) that represent other functions are OK. u' = v' = Now write the first order system using matrices: d 4:]-[ = dt υ The initial value of the vector valued solution for this system is: u(1) v(1) = Ա 18-1 +
Consider the second order differential equation with initial conditions u" 2.5u' + 6.5u = = -7.5 sin(3t), u(1) = -5.5, u'(1) = -4. Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the "velocity function" u'. Do not use u(t) or v(t) to represent these functions. Expressions like sin(t) that represent other functions are OK. u' = v' = Now write the first order system using matrices: d 4:]-[ = dt υ The initial value of the vector valued solution for this system is: u(1) v(1) = Ա 18-1 +
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 solve it on the paper
![Consider the second order differential equation with initial conditions
u" - 2.5u' +6.5u
-7.5 sin(3t),
u(1) = -5.5,
Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single
letter u to represent the function u and the single letter v to represent the "velocity function" u'. Do not use u(t) or v(t) to
represent these functions. Expressions like sin(t) that represent other functions are OK.
u'
v' =
Now write the first order system using matrices:
[:]-[
The initial value of the vector valued solution for this system is:
dt
u(1)
v(1)
|
=
=
u²(1):
= -4.
][:]-[
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2Fc9f11f64-3de4-4721-92ca-f50bf94c60a3%2Ftmvzzc_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the second order differential equation with initial conditions
u" - 2.5u' +6.5u
-7.5 sin(3t),
u(1) = -5.5,
Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single
letter u to represent the function u and the single letter v to represent the "velocity function" u'. Do not use u(t) or v(t) to
represent these functions. Expressions like sin(t) that represent other functions are OK.
u'
v' =
Now write the first order system using matrices:
[:]-[
The initial value of the vector valued solution for this system is:
dt
u(1)
v(1)
|
=
=
u²(1):
= -4.
][:]-[
+
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