+0

0
60
4

dx/dt = x-2y

dy/dt = x+4y

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

Aug 20, 2019

#1
+5788
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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
0

can you just help me to rewrite it as you mentioned in the first step please?

Guest Aug 21, 2019
#3
+5788
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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
0

You the best! Thank you.

Guest Aug 21, 2019