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.

Guest Aug 20, 2019

#1**0 **

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

.Rom Aug 20, 2019