- #1

RJLiberator

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## Homework Statement

This is an ordinary differential equation using the differential operator.

Given the system:

d^2x/dt - x + d^2y/dt^2 + y = 0

and

dx/dt + 2x + dy/dt + 2y = 0

find x and y equation

Answer: x = 5ce^(-2t)

y = -3ce^(-2t)

## Homework Equations

## The Attempt at a Solution

We change it into a differential operator equation...

[D^2-1]x+[D^2+1]y = 0

[D+2]x +[D+2]y = 0

We simply cancel values out until we are left with

3x+5y = 0

[D+2]x +[D+2]y = 0

Here we have x = -5y/3 and y = -3x/5

We substitute into the second equation and we can easily find that

x = ce^(-2t)

y = ce^(-2t)

My question is: How does the answer book know that there is a 5 for the x equation and a -3 for the y equation. It seems to me that the constant "c" handles this for me.

Am I doing something wrong to get a less precise answer? Or did I work out this problem correctly.

Thank you.