Using the laplace transform, find the solution to the differential equation:(adsbygoogle = window.adsbygoogle || []).push({});

y'' + y' + y = 0 , y(0)=0, y'(0)=1

Using the laplace transform and its properties I end up with:

f(s) = 1/(s^{2}+s+1)

How can I find the inverse of this/ does anyone know the inverse of it?

Setting y=e^{ax}I got a characteristic equation of a^{2}+a+1=0, which has a complex solution, so I suspec that the inverse above should be a combination of both a sine, cosine and an exponential..

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# Inverse laplace transform

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