Please help me, I want to graph this attached simple relation

[Paul]

What code have you tried so far?

[Torsten]

Define the constants.

Define X (e.g. as X = -6:0.0001:6) .

Define phi.

Use plot(X,phi) to plot.

To get used to MATLAB, you should pass MATLAB Onramp - a course free of costs to learn the basics of the new software:

https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

[Torsten]

As said: pass the introductory MATLAB course. Otherwise your attempts to use the software will lead to nothing.

a0 = 0.1; a1 = 0.1; c1 = 1; c2 = 0.1; c3 = 0.1; c4 = 0.5; lambda = 4; mu = 1;
x = -6:1/10000:6;
phi = a0 + a1*(c1*cosh(sqrt(lambda^2-4*mu)/2*x)+c2*sinh(sqrt(lambda^2-4*mu)/2*x))./...
              (c4*cosh(sqrt(lambda^2-4*mu)/2*x)+c3*sinh(sqrt(lambda^2-4*mu)/2*x));
plot(x,phi)

Answer 1

[Matt J]

The following is deliberately not exactly what you asked for, but illustrates one possible approach.

 [a0,a1,c1,c2,c3,c4,lambda,mu]=deal(31/100, 19/20,  19/25,7/100,61/100,12/25,  3,17/50 );

 x = (-3:0.001:+4)';

 z=(sqrt(lambda^2 - 4*mu)/2).*x;

 B=[sinh(z), cosh(z)]*[c1, c4; 
                       c2, c3];
 
 y=a0+a1*B(:,1)./B(:,2);

 plot(x,y);  ylim([-10,10]); xlabel('x'); ylabel('$\varphi(x)$',Interpreter='latex')

●

[Tarek]

Hellow Mr @ Matt J. Thanks for alot.

Does the sequence of constants in the matrix b correct such that the constants C1 multiplied by cosh, C2 sinh, c3 sinh and c4 * cosh ??

[Matt J]

As I said, it's deliberately not exactly what you asked for. I don't promise that the coefficients have been applied as in your original problem.

Answer 2

[Walter Roberson]

The following is deliberately not exactly what you asked for, but illustrates the techniques you would use.

Q = @(v) sym(v);
a_0 = Q(round(rand,2))

a_0 = 

a_1 = Q(round(rand,2))

a_1 = 

c_1 = Q(round(rand,2))

c_1 = 

c_2 = Q(round(rand,2))

c_2 = 

●

c_3 = Q(round(rand,2))

c_3 = 

c_4 = Q(round(rand,2))

c_4 = 

lambda = Q(3);
mu = Q(round(rand,2))

mu = 

syms x
num1 = cosh((sqrt(lambda^2 + 3*mu)/2) * x);
num2 = sinh((sqrt(lambda^2 - 2*mu)/2) * x);
den1 = num2;
den2 = num1;
phi(x) = a_0 + a_1 * (c_1 * num1  + c_2 * num2) / (c_3 * den1 + c_4*den2)

phi(x) = 

fplot(phi, [-3 7])

[Tarek]

Hello Walter Roberson

when run this above code, this message error. Please help me

%Error using sym/subsasgn (line 64)

Error using maplemex

Error, (in MTM:-subsasgn) unsupported type of index, x

Error in Untitled3 (line 15)

phi(x) = a_0 + a_1 * ((c_1 * num1 + c_2 * num2) / (c_3 * den1 + c_4*den2));

%% code

syms x;
Q = @(v) sym(v);
a_0 = Q(round(rand,2))

a_0 = 

a_1 = Q(round(rand,2))

a_1 = 

c_1 = Q(round(rand,2))

c_1 = 

c_2 = Q(round(rand,2))

c_2 = 

c_3 = Q(round(rand,2))

c_3 = 

c_4 = Q(round(rand,2))

c_4 = 

lambda = Q(3);
mu = Q(round(rand,2));
num1 = cosh((sqrt(lambda^2 + 3*mu)/2) * x);
num2 = sinh((sqrt(lambda^2 - 2*mu)/2) * x);
den1 = num2;
den2 = num1;
phi(x) = a_0 + a_1 * ((c_1 * num1  + c_2 * num2) / (c_3 * den1 + c_4*den2));
fplot(phi, [-3 7])

[Walter Roberson]

@Tarek

You appear to be using the MATLAB Connector for Maple -- in other words you have formed a link between MATLAB and Waterloo Maple, to have Maple act as the symbolic engine.

The replacement statement for

phi(x) = a_0 + a_1 * ((c_1 * num1  + c_2 * num2) / (c_3 * den1 + c_4*den2));

is

phi = symfun(a_0 + a_1 * ((c_1 * num1  + c_2 * num2) / (c_3 * den1 + c_4*den2)),x);

I no longer recall whether Maple supports fplot()

[Sam Chak]

Hi @Tarek

If you receive an "Error using maplemex", this indicates that there is an issue with the Maple engine running code from within MATLAB. This article suggests a workaround that you may find helpful: Maple-MATLAB Connector Error.

If you are already familiar with Maple, wouldn't it be easier to plot the graph directly in Maple? This approach eliminates the need to run the Maple code from within MATLAB. Furthermore, why did you not assign these constants directly in your code?

a0      = 0.1; 
a1      = 0.1; 
c1      = 1; 
c2      = 0.1; 
c3      = 0.1; 
c4      = 0.5; 
lambda  = 4; 
mu      = 1;