Mathematics - Differential Equations - Systems of differential equations - Systems via Eigenvalues

10 steps: (1) System: x'=Ax where x is a vector and A is a matrix. (2) Example: x'=2x+y, y'=x+2y → x'=[[2,1],[1,2]]x. (3) Solution: x(t) = c₁v₁e^(λ₁t) + c₂v₂e^(λ₂t) where λ,v are eigenvalues/eigenvectors of A. (4) Find eigenvalues of [[2,1],[1,2]]: λ=3,1. (5) Eigenvectors: for λ=3: v=(1,1). For λ=1: