CHAPTER 5: Introduction to Systems and PhasePlane AnalysisEXERCISES 5.2:Elimination Method for Systems, page 2501.Subtracting the second equation in the system from the first one, we eliminateyand obtainx+y=−2y,y=x−2y⇒x=−x.This equation is separable (also, it is linear). Separation yieldsdxx=−dt⇒ln|x|=−t+C⇒x(t) =c2e−t.Substituting this solution into the second equation, we obtain an equation fory:y+ 2y=x=c2e−t.This equation is a first order linear equation. Solving we obtain
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