How to Plot a second derivative equation?

Question

Guan-Lin Chen 2020-11-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/642600-how-to-plot-a-second-derivative-equation

评论： Star Strider 2020-11-10

采纳的回答： Star Strider

在 MATLAB Online 中打开

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?

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David Wilson 2020-11-10

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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 2020-11-10

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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Answer 1

Star Strider 2020-11-10

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/642600-how-to-plot-a-second-derivative-equation#answer_539535

在 MATLAB Online 中打开

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