Solving a complicated symbolic equation

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.

[John D'Errico]

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

Answer 1

[Matt J]

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

Answer 2

[Pramil]

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