Write the given second order equation as its equivalent system of first order equations u''-8u'-4.5u=-3sin(3t), u(t)=6.5, u'(1)=8

Emily-Jane Bray 2020-12-02 Answered
Write the given second order equation as its equivalent system of first order equations
u8u4.5u=3sin(3t), u(t)=6.5, u(1)=8
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Expert Answer

d2saint0
Answered 2020-12-03 Author has 89 answers
Given
u8u4.5u=3sin(3t)
u(t)=6.5
u(1)=8
Let v=u(t)
u=v
Then
v8v4.5u=3sin(3t)
v=8v+4.5u3sin(3t)
Hence
u=v
v=4.5u+8v3sin(3t)
u(1)=6.5, u(1)=v(1)=8
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