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

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SUMMARY

The discussion focuses on plotting the solutions of the differential equation y' = cos(πty) using Maple. The user encountered issues with the dsolve command, which returned no solution, indicating that a closed-form solution likely does not exist. The conversation emphasizes the importance of using the numeric option in dsolve and utilizing commands such as odeplot to visualize the solutions for 21 initial points between 0 and 4.

PREREQUISITES
  • Familiarity with Maple software and its syntax
  • Understanding of differential equations and initial value problems
  • Knowledge of the dsolve command in Maple
  • Experience with plotting functions using odeplot in Maple
NEXT STEPS
  • Learn how to implement the numeric option in Maple's dsolve command
  • Explore the use of the seq command for generating sequences in Maple
  • Investigate the syntax and options available in the odeplot command
  • Study examples of plotting solutions for differential equations in Maple
USEFUL FOR

Students and researchers in mathematics, particularly those studying differential equations, as well as Maple users looking to enhance their plotting skills for numerical solutions.

OrigGan
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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
 
Physics news on Phys.org
(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" ...
 

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