How can I plot the solutions of a differential equation using Maple?

In summary, the problem given is to plot the solutions of y' = cos(pi*ty) for 21 equally distributed initial points between 0 and 4. The provided hint suggests using commands such as seq, dsolve, numeric, odeplot, and display. The conversation also mentions starting off with a given equation and trying to include the "numeric" command in dsolve to find a solution. However, no closed-form solution is found. The hint is reiterated, stating the use of "numeric" and "odeplot" commands, and the need to use "seq" for the given sequence of initial points. The conversation ends with a request for help in putting the plot together and a reminder to write
  • #1
OrigGan
2
0
So I was given the following problem to do in maple:

In one ty-graph plot the solutions of y' = cos(pi*ty) for a sequence of 21 equally distributed initial points y(0) between 0 and 4. Hint: You
may use commands such as seq, dsolve, numeric, odeplot and display.

I started off with:
>x:=diff(y(t),t)=cos(pi*t*y(t))
Then, I did:
>dsolve(x,y(t))
This just gives a blank space, which I read means maple can't find an answer.
From reading some examples online and from the hint above I think I may need to include numeric in dsolve but I can't get that to work without an initial condition.

I also know the sequence will obviously be 0..4,0.2 but then I don't understand what it means by the y(0) part.

Any help in putting this plot together is much appreciated
 
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  • #2
(1) In Maple write Pi not pi

(2) No solution shown, that means Maple did not find a closed-form solution. Probably there is none.

(2) The hint is in the assignment... "numeric" and "odeplot" ...
 

1. What is ODE plotting in Maple ARG?

ODE plotting in Maple ARG refers to using the Maple Advanced Research Graphing (ARG) tool to plot solutions of ordinary differential equations (ODEs). This allows for visualizing and analyzing the behavior of ODEs, which are mathematical equations that describe how a variable changes over time.

2. How does ODE plotting in Maple ARG work?

To plot ODEs in Maple ARG, you first need to define the ODE using the dsolve command and specify initial conditions. Then, use the DEplot command to generate a plot of the solution. You can also customize the plot by specifying the range of values for the variables and adding labels and legends.

3. What types of ODEs can be plotted in Maple ARG?

Maple ARG can plot solutions for a wide range of ODEs, including first-order, second-order, and systems of ODEs. It also supports ODEs with boundary conditions and initial value problems. Additionally, Maple ARG can plot solutions for both analytical and numerical solutions of ODEs.

4. Are there any limitations to ODE plotting in Maple ARG?

While Maple ARG is a powerful tool for visualizing ODEs, it does have some limitations. For example, it may not be able to plot solutions for certain types of ODEs with complex solutions. Additionally, the size and complexity of the ODE may affect the speed and accuracy of the plotting process.

5. Can ODE plotting in Maple ARG be used for research purposes?

Yes, ODE plotting in Maple ARG can be used for research purposes. With its advanced features and customizable options, it is a valuable tool for analyzing and interpreting the behavior of ODEs. It can also be used to generate graphs for research papers and presentations.

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