error on using fplot

Hi, I'm new on matlab and maybe this could be a silly answer. I solved this fourth order differential equation, but I have some problems with the function "fplot(usol(x))". Could anyone help me? Thank you! That's the code:

syms u(x) d

a=0.1

Du=diff(u,x)

D2u=diff(u,x,2)

D3u=diff(u,x,3)

ode=diff(u,x,4)==-4*(a^4)*u

c1=u(0)==d

c2=D2u(0)==0

c3=D2u(1)==0

c4=D3u(1)==0

conds=[c1 c2 c3 c4]

usol(x)=dsolve(ode,conds)

usol(x)=subs(usol(x))

fplot(usol(x));

-------------------------------

I report also the error:

Error using fplot>singleFplot (line 240)

Input must be a function or functions of a single

variable.

Error in

fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args)

(line 200)

hObj = cellfun(@(f)

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

Error in fplot>vectorizeFplot (line 200)

hObj = cellfun(@(f)

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

Error in fplot (line 166)

hObj =

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

Error in fourhordertravesuoloelastico (line 18)

fplot(usol(x));

Answer 1

[Jorg Woehl]

Your solution usol contains two symbolic variables, x and d, but fplot can only deal with functions of a single variable. I suppose that you have forgotten to substitute the value for d, which is probably what you were trying to do in the line usol(x)=subs(usol(x)) - otherwise, this line wouldn't do anything.

For example, this works just fine:

d = 0.2
usol = subs(usol)
fplot(usol)

[Lorenzo Mereu]

Thank you, It worked!!

[Lorenzo Mereu]

I have another question: how to plot the solution for some values of "a"? in other words, I want to find some solutions with the parameter "a" that varies, in the same graph

[Jorg Woehl]

In this case, you could put your code (except for the fplot line) in a function myfun(a) or even myfun(a, dValue), where you supply the needed numerical values. (Note that if want d to remain a symbolic varialbe inside the function, you need to supply its numerical value using another variable dValue).

function usol = myfun(a, dValue)
syms u(x) d
Du = diff(u, x);
...
d = dValue;
usol = subs(usol);
end

Then call your function multiple times to create your plots and add them all to the same graph:

fplot(myfun(0.1, 0.2));
hold on;
fplot(myfun(second_a_value, 0.2));
fplot(myfun(third_a_value, 0.2));