ithout solving it, rewrite the given second order differential equation t'u" - 3.5tu' + (t² − 1)u = −7 sin(3t) an equivalent system of first order differential equations. In your answer use the single letter nd the single letter v to represent the "velocity function" u'. Do not u(t) or v(t) to represent the n(t) that represent other functions are OK.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Without solving it, rewrite the given second order differential equation
as an equivalent system of first order differential 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 u(t) or v(t) to represent these functions. Expressions like
sin(t) that represent other functions are OK.
u'
v'
=
Now write the system using matrices:
[:] 1-1
t²u" – 3.5tu' + (t² − 1)u = −7 sin(3t)
d
dt
][8][
Transcribed Image Text:Without solving it, rewrite the given second order differential equation as an equivalent system of first order differential 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 u(t) or v(t) to represent these functions. Expressions like sin(t) that represent other functions are OK. u' v' = Now write the system using matrices: [:] 1-1 t²u" – 3.5tu' + (t² − 1)u = −7 sin(3t) d dt ][8][
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