u' = Consider the second order differential equation with initial conditions 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. V = u" - 8u8u = -4.5 sin(3), u(1) = -5, u' (1) = -3.5. Now write the first order system using matrices: u d #B]-[ = dt V The initial value of the vector valued solution for this system is: u(1) CH = v(1) u V +
u' = Consider the second order differential equation with initial conditions 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. V = u" - 8u8u = -4.5 sin(3), u(1) = -5, u' (1) = -3.5. Now write the first order system using matrices: u d #B]-[ = dt V The initial value of the vector valued solution for this system is: u(1) CH = v(1) u V +
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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![u' =
Consider the second order differential equation with initial conditions
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.
V =
u" - 8u8u = -4.5 sin(3), u(1) = -5, u' (1) = -3.5.
Now write the first order system using matrices:
u
d
#B]-[
=
dt
V
The initial value of the vector valued solution for this system is:
u(1)
CH
=
v(1)
u
V
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8764cbe2-eeb1-4a85-a232-e8ed74abd77c%2F26538a67-cd94-49c9-8d38-891984b15ca6%2Fyfvudzp_processed.png&w=3840&q=75)
Transcribed Image Text:u' =
Consider the second order differential equation with initial conditions
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.
V =
u" - 8u8u = -4.5 sin(3), u(1) = -5, u' (1) = -3.5.
Now write the first order system using matrices:
u
d
#B]-[
=
dt
V
The initial value of the vector valued solution for this system is:
u(1)
CH
=
v(1)
u
V
+
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