# Math Help - Initial value problem: stuck on detail, help wanted!

1. ## Initial value problem: stuck on detail, help wanted!

Hi there.

I'm stuck solving the following problem, as I'm not sure how to find the values of 'B'. I gather I need to use the original DE, but I'm lost as to how. Can someone please help me out?

Any help would be greatly appreciated.
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Find $V(t)$, when: $k = 0$, and also
$k != 0$.

initial conditions are: V(0) = 0 and V'(0) = 0

$(d^2V/dt^2) + 2 (dV/dt) + V = Vo ( exp(-kt) + 7ksin(t) )$
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This is what I've got so far:

$V'' + 2V' + V = 0$

$(m+1)(m+1)$

$m1 = m2 = -1$

so homogenous eqn is:

$u = A1.exp(-x) + A2.x.exp(-x)$

and non-homog. one is:

$y = B1.exp(-kt) + B2.sin(t) + B3.cos(t)$