How to solve hyperbolic equation with ratio?

1 次查看（过去 30 天）
ld ld
ld ld 2021-8-23
回答： David Goodmanson 2021-9-1
Find out x in following equation in which 'y' and 'z' are known.
( y/z ) = (tanh x)/(tanh (x/z))
evaluate x from the following equation if 'y' and 'z' are known.
  2 个评论
ld ld
ld ld 2021-9-1
yes it is related to it.
Even if it can be solved without matlab, it would be ok.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

David Goodmanson
David Goodmanson 2021-9-1
Hi L^2,
It never hurts to make a plot. Assume for the moment that z >1. Calling the right hand side of the equation f(x), then f(x) is a symmetric function with a peak around x=0, and 1 < f(x) < z. y/z has to fall within that range in order to have a real solution. There are similar results for z <1 and for negative z.
x = -40:.01:40;
z = 4;
y = 10;
f = @(x) tanh(x)./tanh(x/z)
g = @(x) f(x) - y/z;
x0 = fzero(g,[.001 20]) % root = 1.5252
figure(1);grid on
plot(x,f(x),x0,f(x0),'o',x,(y/z)*ones(size(x)))

类别

在 Help Center 和 File Exchange 中查找有关 Contour Plots 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by