How to solve hyperbolic function ratio equation
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find x from the following equation
( y/z ) = (tanh x)/(tanh (x/z))
evaluate x from the following equation if 'y' and 'z' are known.
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Wan Ji
am 23 Aug. 2021
you can solve it with symbolic expression
syms z x y
eq = y/z - tanh(x)/tanh(x/2);
sol = solve(eq, x, 'ReturnConditions',true);
x = sol.x
% conds = sol.conditions % see conditions
x equals to
x =
log((z + (-y*(y - 2*z))^(1/2))/(y - z)) + pi*k*2i
log((z - (-y*(y - 2*z))^(1/2))/(y - z)) + pi*k*2i
where k is an integer.
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Wan Ji
am 23 Aug. 2021
Given y=1, z=2, k=0, evalute x as
x =[ log((z + (-y*(y - 2*z))^(1/2))/(y - z)); ...
log((z - (-y*(y - 2*z))^(1/2))/(y - z))];
x = subs(x, [y,z],[1,2])
Then
x0 =
log(- 3^(1/2) - 2)
log(3^(1/2) - 2)
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