(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve for u(x):

[tex]0 = e^{2\int u(x) dx} + u(x) e^{\int u(x) dx} - a(x)[/tex]

2. Relevant equations

3. The attempt at a solution

I tried using the quadratic formula,

[tex]e^{\int u(x) dx} = \frac{-u(x) \pm \sqrt{u^2(x) + 4a(x)}}{2}[/tex]

, converting to log notation and differentiating, but from there I didn't know how to solve for u(x). I thought maybe I could use something on the lines of the log-definitions of the inverse trig functions. Any ideas?

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# Integral equation

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