Differential Equations with 1/x

Limits, differentiation, related rates, integration, trig integrals, etc.
Derivitator
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Joined: Tue Apr 17, 2012 11:44 pm
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Differential Equations with 1/x

Postby Derivitator » Wed Apr 18, 2012 12:00 am

Say you have a differential equation like this:

(1/y)dy = dx

When you integrate both sides, you get this:

ln|y| = x + C

Taking e to the both sides...

|y| = e^(x + C)

From here, my teacher says that the answer would simply be y = e^(x + C).
However, taking a simpler situation involving absolute values:

|y| = 1

In this case y = ±1.

1 is always positive, and so is e^(x + C).
So applying this to the above, I would get this instead:

y = ±e^(x + C)

Can anyone explain why the plus or minus is not (or is) needed?

nona.m.nona
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Re: Differential Equations with 1/x

Postby nona.m.nona » Fri Apr 20, 2012 2:13 pm

You may find a useful discussion on page five of this PDF document.


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