On Jan 18, 2009, at 9:06 PM, dgorbachev wrote:

I'm just wondering is there any way to specify initial conditions for an ordinary differential 
equation, for instance dy/dx = ky, y(0) = 2

No initial conditions can be specified explicitly with GC 3.5, however you can move the cross-hair in such a way as to see the curve matching any given initial conditions.

For example, if I wanted to see the curve for which y(2) = 2 (I chose non-zero x so that it wouldn't be hidden by the y axis), just plot lines for x = 2 and y = 2. You want a curve through their intersection.

To see that curve, click on any of the existing curves for the ODE. The cursor will change to a small blue square with dotted "cross-hairs" through it:

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Next, drag the cross-hairs over the green lines. GC will plot a solution curve which follows the cursor. The small numbers in the top left corner of the graphing pane will tell you where you are. 

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Workaround 2: change resolution until you get curve matching initial conditions:

If you search for "ODE Plots" in the online help, you'll get the following page. As you can see, GC chooses initial conditions itself.

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You can change the spacing of the solution curves until you get one matching you're initial conditions (as shown by the green lines) as follows: Make sure that the differential equation is selected, either by selecting the whole equation or just clicking anywhere on it, and then change the resolution by dragging the "resolution slider" at the bottom left until you get a curve going through the green lines:

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If you combine two plots of the same equation, one at high resolution and one at lower resolution (fewer solution curves plotted), you can then in effect highlight the curve you're interested in by using the first technique above, of dragging the cross-hairs over the lines representing the initial conditions:

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