- #1

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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