Can some one help me to solve the following equation for x :It actually popped out of a physics problem that I was solving and is still not solved.
You're very welcome.
Ignore everything above.
Move the inverse hyperbolic tangent term to the RHS
Square both sides
Multiple the 4 in
Divide by 4*roh*A1
What's the heck is h? This significantly changes changes the whole complexity of the question.
Faizan: I don't mean to flog the point but you missed the 2nd part of my response.
In line 15 you have: e^2y = B where B = [sqrt(m) +t] / [sqrt(m) - t]
Then on line 17 you have : 2y = B
This is incorrect as line 15 implies that: 2y = ln(B)
So everything that follows doesn't work.
Wasi: I have discovered another problem:
line 15 is O.K.
I assume p is a density, A is a cross-sectional? area and x is a length?
At any rate, assuming m,p,A are positive line 15 does not have a real solution for positive x as [sqrt(m) +sqrt(m+pAx] / [sqrt(m) - sqrt(m+pAx)] will be negative since
sqrt(m+pAx) > sqrt(m).
This leads directly to ln(negative) which is not real.
Or you can look above:
e^2y can never be negative so e^2y = B(negative) has no real solution.
So I need to know more about I,m,p,A,x actually represent. It looks to me like a physics problem. I need information on the domain (possible x values). Because if x is positive then there is no real solution.
I hate to be the fly in the ointment again, but here's throwing caution to the wind.
In line 15 you have some of the form : e^2y = B.
In log form this become: 2y = ln(B),
not 2y = B which what you have in line 17
You can even take the route of e^2y = e^ln(B) , which is unnecessary, but it still leads to 2y = ln(B). So line 17 is missing the ln function.
The bottom line is you have 2y = ln( a function of y) which does not have an elementary solution. Maybe there is some kind of Lambert function solution but that's the best you have.
Wasi: You might try using the infinite Maclauren series for arc_tanh(x) and use a computer to grind out some desired level of accuracy and then go from there or the Lambert function possibility. I think those 2 are your only shot.
Thanks for pointing out the typo error The updated solution is here.