Consider the system of differential equations dx/dt=y dy/dt= 2x-y. Write the system in matrix form and find the eigenvalues and eigenvectors for the matrix.

Answer 1

The Characteristic Equation being λ² +λ -2 = 0,

the eigenvalues are λ = 1 and λ = -2

and the corresponding eigenvectors x₁ = < 1,1> and x₂ = < 1, -2 >

The general solution

x(t) = c₁ e^t +c₂ e^-2t

y(t) = c₁ e^t -2c₂ e^-2t