Solving symbolic partial differential equation

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Ben Holmes 2018-2-27

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https://ww2.mathworks.cn/matlabcentral/answers/385152-solving-symbolic-partial-differential-equation

评论： Ben Holmes 2018-2-27

I am looking to solve a symbolic partial differential equation (PDE), akin to how another symbolic mathematical environment uses the function pdsolve().

Is there an equivalent in the MATLAB symbolic toolbox? I have found dsolve, however am not sure how much of the behaviour would be equivalent.

So far I have only received the error message "Indeterminates must be functions." I am thinking this must be due to how I have set up

f(t1, t2, t3, p2, p3, p4)

In my minimum working example:

%%MWE
syms t1 t2 t3 p2 p3 p4
pars = [t1 t2 t3 p2 p3 p4];
d = 1;
MM = length(pars);
alphapre = [0; 0; -t3/p4; 0; 0; 1];
syms f(t1, t2, t3, p2, p3, p4)
alpha = sym(zeros(d, MM));
PDE = sym(zeros(d,1));
for mm = 1:d
    alpha(mm, :) = alphapre(:,mm).';
    PDE(mm) = sum(alpha(mm,:).*jacobian(f,pars));
end
dsolve(PDE == 0);

which results in a PDE of the form

                                      d
                                  t3 --- f(t1, t2, t3, p2, p3, p4)
   d                                 dt3
  --- f(t1, t2, t3, p2, p3, p4) - -------------------------------- == 0
  dp4                                            p4

The answer to this example should be

t3*t4

Have I made a stupid mistake? Or is it just that I should use something different for this functionality?