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mathman44
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Homework Statement
Find a continuous y(t) for t > 0 to the initial value prob:
[tex]y'(t)+p(t)y(t)=0, y(0)=1[/tex]
where
[tex]p(t)=2[/tex] for 0 < t < 1
[tex]p(t)=1[/tex] for t > 1
and determine if the soln is unique.
The Attempt at a Solution
By standard ODE techniques I arrive at
[tex]y=\exp(-2t)[/tex] for 0 < t < 1
[tex]y=\exp(-t)[/tex] for t > 1
The problem is that this soln y(t) isn't continuous.. what's wrong here? As far as I know the only way to do this is to solve for y(t) in both intervals of t.
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