How to Plot a second derivative equation?

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?

[David Wilson]

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]

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?

Answer 1

[Star Strider]

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!

[Guan-Lin Chen]

It works!

Thank you!!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

[Guan-Lin Chen]

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?

[Star Strider]

No.

First, the other variables need to be declared:

syms x_1 x_2 equ(t) w_2 a_2 B_2 r_2 
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;

and second, ‘equ_1’ and ‘equ_2’ must be functions of only one variable,. so the others must have scalar numeric values.

Then you can plot them using fimplicit.

[Guan-Lin Chen]

Thank you!

I use the code and get error like this

Error using fimplicit>singleFimplicit (line 179)

Input must be a function or functions of a single variable.

Error in fimplicit>@(f)singleFimplicit(cax,f,limits,extraOpts,args) (line 148)

hObj = cellfun(@(f) singleFimplicit(cax,f,limits,extraOpts,args),fn,'UniformOutput',false);

Error in fimplicit>vectorizeFimplicit (line 148)

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]

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!