Differential Equations Help (1 Viewer)

[frenzal_dude]

Hi.


y'' + 2vy' + w^2y = 0

r = +/- iw

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if r = p +/- iq
then p = 0 and q = w
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y(t) = (Ae^pt)cosqt + (Be^pt)sinqt

therefore y(t) = Acoswt + Bsinwt

right?
but in my text book "On the shoulders of Giants" by Smith and McLelland it says:

y(t) = Acost + Bsint, why does w = 1?

 

[Affinity]

maybe you should read your book carefully perhaps you missed a line or soemthing

for one thing, how does r fit into the question? Others don't have the book you have, nor must they use the same conventions for variables.. so what 'r' stands for should be explained.

 

[frenzal_dude]

r is the roots of the auxiliary equation, in this case the auxiliary equation would be: r^2 + 2vr + w^2 = 0,
sorry I forgot to mention 2v = 0,
so the auxiliary equation is actually r^2 + w^2,
where w^2 is c
so the roots are +/- iw,
sorry now the question should sound more understandable.

EDIT:

ahh its cool now, i worked it out, the example didn't have w^2 in it, it had 1.