Solve ODE Plotting for y' = cos(pi*ty) in Maple | Step-by-Step Guide

[OrigGan]

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 am pretty sure 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

 

[mmwave]

.

Hello there,

Thank you for reaching out for help with your problem in Maple. I am a scientist and I would be happy to assist you in solving this problem.

Based on the information provided, it seems like the main issue is that the dsolve command is not giving you a solution. This could be due to the fact that the differential equation is not explicitly defined in terms of y(t). In order to get a solution, you will need to provide an initial condition.

For this specific problem, the initial condition is y(0) = 0. This means that at t=0, the value of y is 0. You can include this initial condition in the dsolve command as follows:

>dsolve({x,y(0)=0},y(t));

This should give you a solution for y(t). Now, to plot the solutions for a sequence of 21 equally distributed initial points between 0 and 4, you can use the numeric and odeplot commands. Here is an example code:

>sol:= dsolve({x,y(0)=0},y(t)); #solves the differential equation with the initial condition
>seq(odeplot(sol,[t,y(t)],t=0..4,stepsize=0.2,y=0..4),i=1..21); #plots the solutions for 21 equally distributed initial points

I hope this helps you in creating the plot you need. Let me know if you need any further assistance. Good luck!

 

[oswaler]

Hello! I am happy to provide a step-by-step guide to help you solve this ODE and plot the solutions in Maple.

Step 1: Define the ODE
First, we need to define the ODE using the diff command, just as you did in your attempt. However, we also need to specify the dependent variable, which in this case is y(t). So the correct command would be:

>ode:=diff(y(t),t)=cos(pi*t*y(t))

Step 2: Solve the ODE
Next, we need to use the dsolve command to solve the ODE. However, as you mentioned, we need to provide an initial condition for the solution. Since we are plotting solutions for a sequence of 21 equally distributed initial points between 0 and 4, we can use the seq command to generate these initial conditions. The syntax for seq is seq(expression, variable = start..end, step). So the command would be:

>solutions:=dsolve({ode, y(0)=seq(i/5,i=0..20,1/5)},numeric)

This command will generate 21 solutions with initial conditions y(0) ranging from 0 to 4 in steps of 0.2. The numeric option is used to specify that we want numerical solutions.

Step 3: Plot the solutions
Now that we have the solutions, we can use the odeplot command to plot them. The syntax for odeplot is odeplot(solutions, t = start..end, y = start..end). So the command would be:

>odeplot(solutions, t = 0..4, y = 0..4)

This will plot all 21 solutions in one graph, with t ranging from 0 to 4 and y ranging from 0 to 4.

Step 4: Display the plot
Finally, we can use the display command to display the plot. The syntax for display is display(plot1, plot2, ...). So the command would be:

>display(odeplot(solutions, t = 0..4, y = 0..4))

This will display the plot in a separate window.

I hope this step-by-step guide helps you solve the ODE and plot the solutions in Maple. Let me know if you have any other questions or need further clarification. Keep up the good work with your scientific endeavors!