Systems of Frst-order differential equations151Figure 4.6.Consider the frst equilibrium line. Along this line we have combinations oFxandyFor which ˙x=0. But this means that For any value oFxon this line,xcannot bechanging. This inFormation is shown by the vertical dotted lines in fgure 4.6 Forany particular value oFx. Similarly, For the line denoted˙y=0(y=2x)the value oFyon this line cannot be changing. This inFormation is shown by thehorizontal dotted lines in fgure 4.6 For any particular value oFy.Next consider points either side oF the equilibrium lines in the phase plane. Tothe right oF thex-line we havey<x3implying˙x>0Hence, For any point at whichxlies below thex-line, thenxis rising. Two areshown in fgure 4.6 by thehorizontalarrows that are pointing to the right. By thesame reasoning, to the leFt oF thex-line we havey>x3implying˙x<0Hence, For any point at which
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