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

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To plot the solutions of the differential equation y' = cos(πty) in Maple, start by defining the equation correctly and using the dsolve command with the numeric option due to the absence of a closed-form solution. The initial conditions should be set for a sequence of 21 equally spaced points from 0 to 4, which can be generated using the seq command. The odeplot command is essential for visualizing the solutions based on these initial conditions. It is important to ensure that π is written correctly in Maple to avoid syntax errors. This approach will help in successfully plotting the required 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" ...
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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