MAT244-2013S > MidTerm

MT Problem 5


Victor Ivrii:
Solve the system of ordinary differential equations

Matthew Cristoferi-Paolucci:
Heres my solution

Jeong Yeon Yook:

Rudolf-Harri Oberg:
We begin by finding eigenvalues for the systems matrix. We solve $(5-\lambda)(-4-\lambda)+18=\lambda^2-\lambda-2=0$. This yields $\lambda_1=2, \lambda_2=-1$. We now search for eigenvectors.

For $\lambda_1=2$, the eigenvector is $\xi_1=(1,1)$

For $\lambda_2=-1$, the eigenvector is $\xi_2=(1,2)$.

General solution for the system is $Y_G=c_1e^{2t}\xi_1+c_2e^{-t}\xi_2$

Devangi Vaghela:
This is my solution


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