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 Frst one, we eliminateyand obtainx0+y0=−2y,y0=x−2y⇒x0=−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:y0+2y=x=c2e−t.This equation is a Frst order linear equation. Solving we obtainµ(t)=exp
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.