MATLAB: Matlab Error: “The solutions are parametrized by the symbols” when solving an Equation

equationMATLABsolve

Here you can better see the equation i'm trying to solve. It's one hyperbolic equation of an ellipse with one unknown variable. I know the result to be +-0.508, but i want to calculate it with Matlab. It's my first time solving an intricate equation in Matlab.
So i input the following code in Matlab R2014a:
 >> syms epsilon
 >> eqn =  (-0.089455)^2 / ( sinh(0.2*asinh(1/epsilon)) )^2   +  (0.9900671)^2 / (cosh(0.2*asinh(1/epsilon)) )^2  == 1;
 >> solve(eqn, epsilon)
and i get the following output:
 Warning: The solutions are parametrized by the symbols:
z2 = Dom::ImageSet((5*log(z1))/2 + 10*PI*k*I, [k, z1], [Z_, RootOf(z^4 - (284839362933894611*z^3)/72057594037927936 + (208168816378854957*z^2)/36028797018963968 -
(284839362933894611*z)/72057594037927936 + 1, z)]) minus Dom::ImageSet(PI*k*I, k, Z_) union Dom::ImageSet(5*log(-z1^(1/2)) + 10*PI*k*I, [k, z1], [Z_, RootOf(z^4 -
(284839362933894611*z^3)/72057594037927936 + (208168816378854957*z^2)/36028797018963968 - (284839362933894611*z)/72057594037927936 + 1, z)]) minus Dom::ImageSet(PI*k*I, k, Z_)
 > In solve at 190 
 ans =
 1/sinh(z2)
No matter what i do i can't make this to work. It's very strange. Any help will be greatly appreciated. Thanks in advance.

Best Answer

There is no error there: it is a warning.
You should have a look at 'ReturnConditions' and 'MaxDegree'
It does not really make sense to be asking for a closed form solution for equations that involve floating point values. You should be considering using vpasolve() instead of solve()
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