# I want to find 4 constant with used 1 eq

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Arash_ORD on 21 Aug 2022
Commented: Arash_ORD on 27 Aug 2022
Hello guy
How can I find 4 constant with used 1 equation?
My eq is ''ydata=x1*(1-exp(-x2*516))+x3*(exp(x4*516)-1)'' and I just have a ydata.
ydata=0.269
x1 x2 x3 x4 are my constant.
Thanks

John D'Errico on 27 Aug 2022
I'd like to solve a problem just like you. Let me pretend I have been given the equation:
a + b + c + d = 5
Can I determine all 4 variables? Is there any way I can learn the value of all 4 variables, given ONLY that one equation? So one data point only? The answer of course is no. At best you can pick the value of any three of those variables. Set them equal to any number you want. Then you can solve for the one variable you have not specified. That is the fundamental nature of an underdetermined problem - the one equation does not provide sufficient information.
If you have MULTIPLE data points, this becomes a different question. So if you have sufficient data points, then you can solve the problem. But you have said you have only one data point. (And I'm sorry, but the nice flowchart you have shown in a comment is not going to make the mathematics work.) An underdetermined problem is just that.

Alan Weiss on 21 Aug 2022
Edited: Alan Weiss on 21 Aug 2022
This is an underdetermined problem, meaning there are many different values of x1, x2, x3, and x4 that work. For example, choose any nonzero value for x2, and then you can solve for x1 given any values of x3 and x4:
Alan Weiss
MATLAB mathematical toolbox documentation
Arash_ORD on 27 Aug 2022
Hello Mr. @John D'Errico.

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