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dx/dt = x-2y 

dy/dt = x+4y 

 

this is is a system of differential equations that need to be solved using matrix method. 

Can you please help me with it? Thank you. 

 Aug 20, 2019
 #1
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\(1)~\text{rewrite the system as $u^\prime = A u,$ where $u(t)=\begin{pmatrix}x(t)\\y(t)\end{pmatrix}$}\\ 2) ~\text{find the eigenvalues $\lambda_{1,2}$ and corresponding eigenvectors $v_{1,2}$ of $A$}\\ 3) ~u(t) = c_1 e^{\lambda_1 t}v_1 + c_2 e^{\lambda_2 t}v_2\)

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 Aug 20, 2019
edited by Rom  Aug 20, 2019
 #2
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can you just help me to rewrite it as you mentioned in the first step please?

Guest Aug 21, 2019
 #3
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\(\dfrac{du}{dt} = \begin{pmatrix}\dfrac{dx}{dt}\\\dfrac{dy}{dt}\end{pmatrix} = \begin{pmatrix}1&-2\\1&4\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix} = A u\)

Rom  Aug 21, 2019
 #4
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You the best! Thank you. 

Guest Aug 21, 2019

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