How to Plot a second derivative equation?

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Hi all,
The equation I want to plot is
I've tried to gether information online and come up with the code:
clc
clear
syms x(t)
Dx = diff(x);
D2x = diff(x,2);
w = 1
dt = 1/1000;
t = 0:dt:1000*dt;
equ = D2x + (Dx)^3 + x(t)^2 *Dx + x(t) == 0;
figure
fplot(equ)
How to plot the graph with the time interval t?
Edit:
To plot the 2 equation and plot them on the same graph
Can I use the code like this:
syms x_1 x_2 equ(t)
Dx_1 = diff(x_1);
D2x_1 = diff(x_1,2);
Dx_2 = diff(x_2);
D2x_2 = diff(x_2,2);
w_1 = w_2 = 1
a_1 = a_2 = 1
B_1 = B_2 = 1
r_1 = r_2 = 1
equ_1 = D2x_1 + (a_1*(Dx_1) + B_1*x_1^2 - r_1 )*Dx_1 + w_1^2*x_1;
equ_2 = D2x_2 + (a_2*(Dx_2) + B_2*x_2^2 - r_2 )*Dx_2 + w_2^2*x_2;
figure
fimplicit(equ_1, [-1 1]) % Use _fimplicit1 To Plot ‘equ(t)=0’
hold on
fimplicit(equ_2, [-1 1])
grid
Would the graph plot with this code be the solution of the equation?
  2 Comments
David Wilson
David Wilson on 10 Nov 2020
Are you sure this is what you want to solve? Given that you have given us the explicit solution for x(t), why not just plot that?
However, I'm not sure that this is correct. Here is your (posulated) solution for x(t):
clear
syms t real
w=1;
x = exp(-1i*w*t) + exp(1i*w*t)
Now, does this satisfy your ODE?
Dx = diff(x,t)
D2x = diff(x,2)
res = D2x + (Dx)^3 + x^2*Dx + x
r = simplify(res)
Now that gives us which does not equal zero like it should for al t.
Guan-Lin Chen
Guan-Lin Chen on 10 Nov 2020
So, can we plot the graph without knowing x(t)?
That is, to plot the
equ = D2x + (Dx)^3 + x(t)^2 *Dx + x(t) == 0;
directly?

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Accepted Answer

Star Strider
Star Strider on 10 Nov 2020
Try this:
syms x(t) equ(t)
Dx = diff(x);
D2x = diff(x,2);
w = 1
% dt = 1/1000;
% t = 0:dt:1000*dt; % Not needed Here
equ = D2x + (Dx)^3 + x(t)^2 *Dx + x(t);
equ(t) = subs(equ, x, {exp(-1i*w*t)+exp(1i*w*t)}) % Substitute Expression For
figure
fimplicit(equ, [-1 1]) % Use ‘fimplicit’ To Plot ‘equ(t)=0’
grid
The plot is absolutely not interesting, however the code runs without error!
  6 Comments
Guan-Lin Chen
Guan-Lin Chen on 10 Nov 2020
Thank you!
I use the code and get error like this
Input must be a function or functions of a single variable.
hObj = cellfun(@(f) singleFimplicit(cax,f,limits,extraOpts,args),fn,'UniformOutput',false);
hObj = cellfun(@(f) singleFimplicit(cax,f,limits,extraOpts,args),fn,'UniformOutput',false);
Error in fimplicit (line 126)
hObj = vectorizeFimplicit(cax,fn,limits,extraOpts,args);
How to fix it?
Star Strider
Star Strider on 10 Nov 2020
Quoting from my previous Comment:
‘... and second, ‘equ_1’ and ‘equ_2’ must be functions of only one variable,. so the others must have scalar numeric values.’
That is how to fix it!

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