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Solving a complicated symbolic equation

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Orel
Orel 2023-6-2
评论： John D'Errico 2023-6-2
Hello,
im trying to solve the following equation, A=B*x*sinh(x) (A and B are known constants) using symbolic toolbox:
syms x;
A=3;
B=9;
equation=A==B*x*sinh(x);
solution=solve(equation,x)
however i cannot find a solution.
i've tried using vpasolve as well but it still doesnt work.
will appreciate any advice.
  1 个评论
John D'Errico
John D'Errico 2023-6-2
Ran in:
solve fails, because there is no algebraic solution to your problem. However, both fzero and vpasolve will work, and the two answers you have gotten tell you that.
We cannot know why you think vpasolve failed, because we do not see what you tried. But vpasolve does not even desperately need a starting point. (It uses zero as I recall by default.) But a starting point is always a good idea.
syms x;
A=3;
B=9;
equation=A==B*x*sinh(x);
solution=vpasolve(equation,x)
solution = 
0.56248044921102851906187057960428

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回答（2 个）

Matt J
Matt J 2023-6-2
编辑：Matt J 2023-6-2
Ran in:
A=3;
B=9;
f=@(x)A-B*x*sinh(x);
[x,fval]=fzero(f,[0,10]) %first solution
x = 0.5625
fval = 1.3323e-15
[x,fval]=fzero(f,[-10,0]) %second solution
x = -0.5625
fval = 1.3323e-15
Pramil
Pramil 2023-6-2
Ran in:
You can do the following :
syms x;
A = 3;
B = 9;
solution = vpasolve(B*x*sinh(x)==A, x, 1)
solution = 
0.56248044921102851906187057960428
The vpasolve function allows you to specify a starting value for the numerical solver, in this case, the starting value is 1. The output of this code will give you a single numerical value for x

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