Setting

Description

Solution Dir.

A solution curve is graphed starting at the initial condition value t0 and continues until

 

it reaches a target value, which can be either tmin or tmax. The solution direction

 

determines the target values. Forward will graph the solution curve from t0 to tmax.

 

Backward will graph the solution curve from t0 to tmin. Both will graph the solution curve

 

from t0 to tmin, and then t0 to tmax.

 

 

Independent

Assignment of the independent variable for differential equations

 

1st-order, Nth-order: x or t

 

2nd-order: t (fixed)

 

 

t0 (or x0)

If the independent variable is different from the x-axis variable, you can enter the initial

 

value for the independent variable (2nd-order and Nth-order only).

 

 

tmin (or xmin),

If the independent variable is different from the x-axis variable, you can enter the

tmax (or xmax)

minimum/maximum value for the independent variable (2nd-order and Nth-order only).

 

 

x-Axis

Variable assignment for the (horizontal) x-axis

 

1st-order: same as independent variable

 

2nd-order: x (fixed)

 

Nth-order: independent variable or y1 through y10

 

 

y-Axis

Variable assignment for the (vertical) y-axis

 

1st-order, 2nd-order: y (fixed)

 

Nth-order: independent variable or y1 through y10

 

 

5-2 Drawing f(x) Type Function Graphs and Parametric Function Graphs

f(x) type function graphs and parametric function graphs can be overlaid on differential equation graphs.

uTo draw an f(x) type function graph

0506 To overlay a differential equation graph with the graphs of y = x2 and y = −x2

uTo draw a parametric function graph

0507 To graph {xt = 3sin(t) + 1, yt = 3cos(t) + 1} (Angle unit setting: radian, 0 s t s 2π)

5-3 Using Trace to Read Graph Coordinates

The trace function let you read the coordinates on graphs drawn with the Differential Equation Graph application. There are three types of trace: “point trace” (shows the coordinates of any point), “field trace” (shows the coordinates of center of each field line), and “graph/curve trace” (shows the coordinates of points on a graph or solution curve).

uTo start a point trace

On the Differential Equation Graph window, tap K.

uTo start a field trace

Draw a slope field (see page 119) or a phase plane (see page 120), and then tap L.

Chapter 5: Differential Equation Graph Application

123