Solutions of the differential equation for the over-damped case

swimforever
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λ=-(1/2τ)±√[(1/4∏^2)-(ω^2)]
I'm supposed to write the solutions of the differential equation for the over-damped case. The overdamped case is where ω<(1/2τ). I don't know how to write the solution.
I know that when ω=(1/2τ) we get the stuff under the square root to equal zero, but I am unsure of what happens or what the solution is when it's less than that.
 
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It would be helpful if you would show the differential equation to us.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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