Plotting General Solution Of Differential Equation

Question

Fahad Ramzan 2021-5-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/837633-plotting-general-solution-of-differential-equation

编辑： Paul 2021-5-23

It's Giving Many Errors and not plotting the graph. Am unable to indentfy what to do next. The error are as following

Error using fplot>singleFplot (line 227)

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

Error in fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 191)

hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot>vectorizeFplot (line 191)

hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot (line 161)

hObj = vectorizeFplot(cax,fn,limits,extraOpts,args);

Error in Untitled (line 15)

fplot(sol,[-10 10])

clc

clear all

syms y(x)

D4y = diff(y,4)

D3y = diff(y,3)

D2y = diff(y,2)

Dy = diff(y)

eq= D4y +(2.*D3y)+(11.*D2y)+(2.*Dy)+(10.*y)

sol = dsolve(eq)

C1=-1

C2=-1

C3=-1

C4=-1

fplot(sol,[-10 10])

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Answer 1

Torsten 2021-5-23

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编辑：Torsten 2021-5-23

Maybe

sol = dsolve(eq);

sols = subs(sol,[C1,C2,C3,C4],[-1,-1,-1,-1]);

fplot(sols,[-10,10])

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Fahad Ramzan 2021-5-23

am getting the error Undefined function or variable 'C1'.

Torsten 2021-5-23

If you apparently can't set the free parameters of the solution directly (they are named C1,C2,C3 and C4 from Matlab, I guess), you will have to specify 4 boundary conditions in order to get a unique solution that can be plotted. Use the "cond" command to do this.

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Answer 2

Paul 2021-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/837633-plotting-general-solution-of-differential-equation#answer_706563

在 MATLAB Online 中打开

Need to add one line of code

syms y(x)

D4y = diff(y,4);

D3y = diff(y,3);

D2y = diff(y,2);

Dy = diff(y);

eq= D4y +(2.*D3y)+(11.*D2y)+(2.*Dy)+(10.*y) == 0;

sol = dsolve(eq) % homogeneous solution

sol =

% need to define Ci as sym objects before using subs()

syms C1 C2 C3 C4

% now substitute

sol = subs(sol,[C1 C2 C3 C4],[-1 -1 -1 -1])

sol =

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Paul 2021-5-23

编辑：Paul 2021-5-23

在 MATLAB Online 中打开

Don't know if it's logical. But I think it works this way because Matlab keeps track of these constants over the course of a session and keeps "incrementing" them. For example, I started a fresh Matlab session on my computer:

syms y(x)
D4y = diff(y,4);
D3y = diff(y,3);
D2y = diff(y,2);
Dy = diff(y);
eq = D4y +(2.*D3y)+(11.*D2y)+(2.*Dy)+(10.*y) == 0;
sol = dsolve(eq) % homogeneous solution
 
sol =
 
C5*cos(x) - C6*sin(x) + C3*cos(3*x)*exp(-x) - C4*sin(3*x)*exp(-x)
 
>> sol = dsolve(2*lhs(eq)==0) % homogeneous solution, sort of different equation
 
sol =
 
C9*cos(x) - C10*sin(x) + C7*cos(3*x)*exp(-x) - C8*sin(3*x)*exp(-x)

If the constants were actually poofed as new variables into the workspace, then user variables could be overwritten or Matlab would have to interrogate the workspace to find non-conflicting names.

In this particular case, I have no idea why the first instance of sol used C3-C6 instead of C1-C4. Very mysterious.

I can't find anything in the doc that explains how to "reset" the constants so they start at C1.

Fahad Ramzan 2021-5-23