Description: The drawing of phase plane method includes analytic method and equal inclination line method. I use the isocline method, because the phase plane method uses only the highest two order system, so the first assumption of a general two order differential equation: X '' +aX '' +bX^2+cX=0 X 'because = (DX' /dx) * (dx/dt) * =X '(DX' /dx).
By substituting differential equations:
X '* (DX' /dx) + aX '+bX^2+cX=0.
Because the slope is k= (DX '/dx). If X '=y is set, then the upper form can be reduced to..:
K=- (b*x^2+c*x+a*y) /y
When the input to any x1, Y1, can be determined (x1, Y1) at the slope of K1, in X1 and derta (program set to 0.001) to determine the X2, X2 and K to the line of intersection of the slope is Y2, it can determine the corresponding K2 (Figure 1). And so on, that is, the small line segment can be approximated by the slope of the phase plane graph.
Suppose the input differential equation is: X '' +X=0
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