Can someone help with this?

Hi I need help plotting the resopnse to this differential equation with 10^4 points. thanks if you can help.

!x!+ cx! + kx + εx3 = Bcost
0 ≤ c ≤ 0.5, −1 ≤ k ≤1, 0 ≤ ε ≤1, B = 8.5 ignore the exclamation points.

[Walter Roberson]

Is "εx3" ε*x3 or ε*x^3 ?

If we are to ignore the exclamation marks, then this seems to be

(1 + c + k) * x + ε*x^3 = B*cost

which is not a differential equation.

[Victor]

the form you wrote it in is correct it is ε*x^3.

[Walter Roberson]

Is it correct then that the equation is

(1 + c + k) * x + ε*x^3 = B*cost

? If so then what do you mean by "response"? This is not an differential equation.

Answer 1

[Walter Roberson]

The equation

(1 + c + k) * x + ε*x^3 = B*cost

can be solved using roots()

roots([epsilon, 0, (1 + c + k), -B*cost])

You then have a plot with three independent variables, c, k, epsilon, together with 3 results per location; 0, 1, or 3 of the results will be real-valued. Plotting this will require a 4 dimensional plot: 3 axes plus 1 result. You need to decide how you want to represent the 4th dimension: options include "color", "marker size", and "transparency".

On the other hand, (c+k) is linear, and the only information that it gives beyond the range (min(c)+min(k)) to (max(c)+max(k)) is in the density of the points. So you might as well drop down a dimension in the plotting

N = 100;
[EPSILON, CK1] = ndgrid(linspace(0,1,N), linspace(1 + 0 + -1, 1 + 1/2 + 1, N));
X = roots([EPSILON, 0, CK1, -B*cost]);

surf(EPSILON, CK1, X(:,:,1));  same for (:,:,2) and (:,:,3) for the three different X values

or something similar (I have not checked the exact dimensions that X will come out as)