Simultaneous differential equations

[mathsteacher]

Can someone please help me to plot the solution curves for a pair of simultaneous diff eqns?  Eg x\' = 2x + y and y\' = x + 2y
x\' and y\' are diff wrt t.

Thanks

[Simon]

Dear mathsteacher,

It is not possible to plot the solution curves for a pair of simultaneous differential equations.  

I would suggest the following:

1. Add a point to the graph
2. Enter the equation y\' = 2y + x
3. Click Startup Options and select Point > OK > OK
4. Now you can see one solution of y\' = 2y + x, drag the point around to see other solutions.

The solution of x\' = 2x + y is simply a reflection of the solution y\' = 2y + x in the line y = x.  

5. Place the point at (2, 0) and draw the reflection of the solution in y=x using the scribble tool.  (This then shows the solution of x\' = 2x + y at (0, 2).)
6. Place the point at (0, 2). Using the Point Tool mark the points of intersection between this solution and the scribbled solution.
7. For clarity now delete the scribbled solution.  You should be left with two points.
8. Repeat this for different coordinates.
9. Join up the points using the scribble tool to see an approximation to the solution of the simultaneous differential equations.

This is clearly not ideal and limited to the case of symmetric DEs.  I will add this as a feature request.

Regards,

Simon