Solving non-linear equation including natural logarithm

Hi guys, I am trying to solve this eqn for y and I am just waiting, Matlab stays busy for some reason. What can I do? Do you think there is a simple way to do it?

syms a b c x y

eqn = (1/b) * (c-y)^(3/2) == a-x-(1/2)*log(1-y/c) 

eqn=rewrite(eqn,'log')

s=solve(eqn,y,'IgnoreAnalyticConstraints',true)

Answer 1

[Jeremy]

Most probably, there is no analytical solution for y in terms of (a,b,c,x). You can solve numerically for y at given values of a,b,c,x by using fzero.

[Ogulcan Acikgoz]

I need to fit my data using this equation and I need to get a, b and c values using this fit with +- error values. Do you have any suggestion? For most of the code and program that I use, I need to write y = something.

[Jeremy]

I would solve for x such that

x = @(y) a - (1/b) * (c-y)^(3/2) - (1/2)*log(1-y/c);

and do a regression for x in terms of a,b,c,y?

[Ogulcan Acikgoz]

It seems a good idea, thank you. I am sure it is very easy but I tried to solve and I could not manage to write the code for regression. Also I tried to use curve fitting toolbox and it gave me an error saying that it is too complex.