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]

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