Consider the second order differential equation with initial conditions u" + 7u' +5u = 2.5 sin(3t), u(1) = 5, u'(1) = 6.5. 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. v= Now write the first order system using matrices: U d BHE + dt V V The initial value of the vector valued solution for this system is: u(1) v(1)
Consider the second order differential equation with initial conditions u" + 7u' +5u = 2.5 sin(3t), u(1) = 5, u'(1) = 6.5. 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. v= Now write the first order system using matrices: U d BHE + dt V V The initial value of the vector valued solution for this system is: u(1) v(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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![Consider the second order differential equation with initial conditions
u" + 7u' +5u = 2.5 sin(3t),
u(1) = 5, u' (1) 6.5.
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 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
18-1
3][:]
dt
The initial value of the vector valued solution for this system is:
u(1)
1
v(1)
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c64d87a-c25a-434d-be5f-398162c6784a%2F776e5d70-8eba-4eb2-abc0-a83a75f6f0d6%2Fwszelb_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the second order differential equation with initial conditions
u" + 7u' +5u = 2.5 sin(3t),
u(1) = 5, u' (1) 6.5.
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 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
18-1
3][:]
dt
The initial value of the vector valued solution for this system is:
u(1)
1
v(1)
+
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