# Absolute Values in Separable Differential Equations

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1. Mar 6, 2015

### patrickbotros

When solving a separable differential equation, my textbook says this:
ln|v-49|=-t/5+C→
|v-49|=e-t/5+C
v=49+ce-t/5
What happened to the absolute values? I think it has something to do with the exponential always being positive.

2. Mar 6, 2015

### SammyS

Staff Emeritus
The equation $\displaystyle\ |v-49|=e^{-t/5+C}\$ is equivalent to
$\displaystyle\ v-49=\pm e^{-t/5+C}\$ $\displaystyle\ v-49=c\, e^{-t/5}\$, where $\ c = \pm\ln(C)$​
So the new constant, c, (lower case) absorbs the ± .

3. Mar 7, 2015

### patrickbotros

Ohhhh. HAHA! That was dumb :)