Write the given second order equation as its equivalent system of first order equations. u" – 7.5u' + 1.5u = -3 sin(3t), u(1) = 0, u'(1) = = 1.5 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices: :三一 u dt V and the initial value for the vector valued function is: 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
Question
Write the given second order equation as its equivalent system of first order equations.
" – 7.5u + 1.5u =
-3 sin(3t),
u(1) :
= 0,
u'(1) = 1.5
Use v to represent the "velocity function", i.e. v = u'(t).
Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.)
u 3=
Now write the
system using matrices:
u
d
dt
V
and the initial value for the vector valued function is:
u(1)
v(1)
Transcribed Image Text:Write the given second order equation as its equivalent system of first order equations. " – 7.5u + 1.5u = -3 sin(3t), u(1) : = 0, u'(1) = 1.5 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u 3= Now write the system using matrices: u d dt V and the initial value for the vector valued function is: u(1) v(1)
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