Solving equation with mathematica

[yashar]

hi
i want to solve this equation
a/x=Cosh[b/x]

i set a=1 and b=5
and use NSolve code but mathematica say it can not solve it. but with maple i get real and imaginary parts.
1-is there another method to solve this equation numerically?
2-can this equation be solve for arbitrary a and b?

thanks

 

[Dale]

NSolve is only for polynomial equations. Use FindRoot instead.

 

[yashar]

it gives me x=25.16 which is incorrect!

 

[SteamKing]

If you rewrite the expression so that COSH(5/x) - 1/x = 0 = f(x) and plot, you will see that f(x) is asymptotic with the x axis. Therefore, there is no x value for which f(x) = 0

 

[Dale]

Plotting it it seems that it does not have any real roots. So I think Maple is wrong, there are no real roots.

PS. SteamKing got it faster!

 

[Dale]

I just found a new function: FindInstance. You can use it to find complex roots. Also, apparently you can specify a complex number for your initial value in FindRoot and it will search for a complex root, which I didn't know before.