Solving Differential Equation System

[sergej21]

Homework Statement

x`=z-y
y`=z
z`=z-x
x(0)=1; y(0)=1; z(0)=1

The Attempt at a Solution

Would be glad to know the steps I need to take.

 

[ehild]

Hi Sergej,

This is a system of first order linear differential equations. Have you learned about them? ehild

 

[ehild]

Seek the solutions in the form

x=Ae^λt
y=Be^λt
z=Ce^λt.

You get a "characteristic equation" for λ, with 3 solutions, real and complex. Substitute back and find A,B,C for all cases. The general solution is a linear combination of these three, match the constants to the initial conditions.


ehild

 

[HallsofIvy]

There are a number of different ways to solve linear systems of equations. If you show no work at all, we have no idea which method you have learned and what help would be appropriate. One method is to write the system as a matrix equation. Can you do that? Another would be to differentiate the equations, eleminating variables until you have a third order equation in a single variable. Have you done that in class?