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

Consider ax''+bx'+cx=0 for b^2-4ac=0 with k= -b/(2a).

Show x=e^(kt) is a solution.

3. The attempt at a solution

x=e^(kt)

x'=(-b/2a)e^((-b/2a)t)

x''=(-b^2/4a^2)e^((-b/2a)t)

Then i plugged these into ax''+bx'+cx=0 and simplified to get e^((-b/2a)t)(-((b^2)/2)+c)=0

I'm stuck at what to do next.

Thank you for any help.

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# Quadratic solution to ode

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