(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Systems of first order equations can sometimes be transformed into a single equation of

higher order. Consider the system

(1) x_{1}' = -2x_{1}+ x_{2}

(2) x_{2}' = x_{1}- 2x_{2}

Solve the first equation for x_{2}and substitute into the second equation, thereby obtaining a second order equation for x_{1}. Solve this equation for x_{1}and then determine x_{2}also.

2. Relevant equations

3. The attempt at a solution

Solving (1) for x_{2}yields:

x_{2}= x_{1}' + 2x_{1}

Substituting into (2) yields:

x_{2}' = x_{1}- 2(x_{1}' + 2x_{1})

Simplifying...

x_{2}' = -3x_{1}- 2x_{1}'

How am I supposed to solve this now with the x_{2}' term there?

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# Homework Help: Systems of First Order Linear Equations

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