# The Differential Equation can be expressed as a system of first order equations ?

1x'''+1x''−9x'−9x=0

can be expressed as a system of first order equations by letting x1=x x2=x' x3=x''. The system has the form X'=AX where A has entries:

A11 = , A12 = , A13 =

A21 = , A22 = , A23 =

A31 = , A32 = , A33 =

### 1 Answer

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- hfshawLv 78 years agoFavorite Answer
You have:

x''' + x'' - 9x' - 9x = 0

or, rearranging:

x''' = -x'' + 9x' + 9x

As the question suggests, let x1 = x, x2 = x' and x3 = x''

Then

x1' = x2

x2' = x3

x3' = 9x1 + 9x2 - x3

In matrix notation, if X is the column vector [x1, x2, x3] then:

X' = A*X

where

A =

[0, 1, 0]

[0, 0, 1]

[9, 9, -1]

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