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Cara Duke

Cara Duke

Answered question

2022-05-18

I have to solve following system of equations:
x = x z + e t , z = 2 x 2 z + 3 e t
I would like to have formula for x' in order to find fundamental matrix and so on. So from above quations I obtain z 2 x = e t , integrate sides and have 2 x = z + e t
So I have system of two first-order differential equation
2 x = z + e t , z = 2 x 2 z + 3 e t
Is it correct?

Answer & Explanation

Krish Finley

Krish Finley

Beginner2022-05-19Added 14 answers

Differentiate the first equation & substitute for z'
x = x z e t = x ( 2 x 2 z + 3 e t ) e t
Now use the first equation to substitute for z = x x + e t ... neaten it up a bit ... we have
x + 2 x + x = 2 e t
So the auxillary equation is λ 3 + 2 λ 2 + λ = 0 and the general solution is
x = A + B e t + C t e t .
Now to obtain the particular solution try x = α t 2 e t ... α = 1

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