Using Newton-Raphson method, find the solution for $e^{frac{x^2}{4vt}} = 1+frac{x^2}{2vt}$
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I need help with solving this difficult fluid dynamic expression. I have tried using rules of logs, symbolab algebra calculator and Wolfram Alpha calculator, and I have got no solution. How would you solve the following expression USING the NEWTON-RAPHSON method for $x$ ? $$e^{frac{x^2}{4vt}} = 1+frac{x^2}{2vt}$$ When solving this USING the NEWTON-RAPHSON method, the solution is: $x=2.2418sqrt{vt}$ I want to know how you could solve the first expression using the NEWTON-RAPHSON method to get the solution. So could someone please provide a step-by-step solution, by using this method please? Note: This question was answered, however it was NOT answered using NEWTON-RAPHSON method. It was answered using the Lambert W function, which is a very long and complicated process as compared to the Newton-Raphso...