Plotting Two First Order ODEs and Two Second Order ODEs

[sara_87]

Homework Statement

I have two questions:
1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1)

2)I have two second order ODES X''=... and Z''=... to solve this, we make the substitutions y(1)=X, y(2)=X', y(3)=Z, and y(4)=Z'
then we have two first order ODEs: y(2)'=... and y(4)'=...
I typed this into Matlab (dydt=[(the equation for y(2)'; the equation for y(4)']) but an error came up since i didnt define y(4). how do i do this?

Homework Equations

The Attempt at a Solution

1) i tried putting:
plot(y(1),y(:,2)), and i also tried plot(y(1),y(2)) but these didnt work.


Any help would be very much appreciated.
Than you.

 

[LeBrad]

Homework Statement

I have two questions:
1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1)

The Attempt at a Solution

1) i tried putting:
plot(y(1),y(:,2)), and i also tried plot(y(1),y(2)) but these didnt work.

Than you.

If you have two vectors x and y, you do plot(x,y). If you have two rows of a matrix Y, you do plot(Y(1,:),Y(2, to plot the first row on the x-axis and the second on the y-axis. Similarly, if you have a matrix with two columns, you use plot(Y(:,1),Y(:,2)). Y(i,j) is the element in the i-th row and j-th column of the matrix Y. The colon (:) indicates to take all elements in that row or column. So Y(1,:) is all elements in the first row of Y.

2)I have two second order ODES X''=... and Z''=... to solve this, we make the substitutions y(1)=X, y(2)=X', y(3)=Z, and y(4)=Z'
then we have two first order ODEs: y(2)'=... and y(4)'=...
I typed this into Matlab (dydt=[(the equation for y(2)'; the equation for y(4)']) but an error came up since i didnt define y(4). how do i do this?

Homework Equations

I don't quite understand what you're saying here. Did you give the solver initial conditions for both equations? If you post the code and error I could be more helpful here.

 

[sara_87]

for (1), they're not matrices, they're just equations in terms of y(1) and y(2).

for (2), I've lost my documents so if i find it i'll post another time.
Thank u.

 

[hamood102]

ghyt y

 

[blue_raver22]

Thank you for your questions. To plot y(2) versus y(1), you can use the "plot" function in Matlab and specify the variables as plot(y(1),y(2)). This will plot the values of y(2) on the y-axis and y(1) on the x-axis.

For the second question, you can define y(4) as another variable and then include it in your dydt function. For example, you can define y(4) as y(4)=Z' and then include it in your dydt function as dydt=[(the equation for y(2)'; the equation for y(4)')]. This should resolve the error you encountered.

I hope this helps. Good luck with your plotting and solving of the ODEs!