Write the given second order equation as its equivalent system of first order equations. u" – 8u – 4.5u = -3 sin(34), u(1) = 6.5, l (1) = 8 Use v to represent the "velocity function", i.e. v = u (1). Use v and u for the two functions, rather than u(t) and v(1). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices: d dt V and the initial value for the vector valued function is: u(1) v(1) II
Write the given second order equation as its equivalent system of first order equations. u" – 8u – 4.5u = -3 sin(34), u(1) = 6.5, l (1) = 8 Use v to represent the "velocity function", i.e. v = u (1). Use v and u for the two functions, rather than u(t) and v(1). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices: d dt V and the initial value for the vector valued function is: u(1) v(1) II
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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Transcribed Image Text:Write the given second order equation as its equivalent system of first order equations.
u" – 8u – 4.5u = –3 sin(31),
u(1) = 6.5,
u (1) = 8
Use v to represent the "velocity function", i.e. v = d (1).
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.)
V =
Now write the system using matrices:
d
V
V
and the initial value for the vector valued function is:
u(1)
v(1)
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