second order differential equation with convolution term
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Solve 4y'' + 4y' +17y=g(t) y(0)=0 , y'(0)=0
your answer will involve a convolution term with g(t).
If there is any confusion in the question just assume yourself what must be right .
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Solution Summary
This solution shows how to solve a second order differential equation with a convolution term g(t).
Solution Preview
First we solve the homogenous case 4y''+4y'+17y = 0
We write the characteristic function 4r2 + 4r +17 = 0, this gives us t1 = -1/2 + 2i and t2 = -1/2 -2i
Fundamental Set of Solutions are y1 = e (-t/2) sin(2t) and y2 = e (-t/2) cos (2t)
So our solution for the homogenous equation is
y(t) = c1e (-t/2) ...
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