Separable Differential Equations

olicoh
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Homework Statement


Suppse dn/dt = 1/10n and n(1)=-2. Separate the differential equation, then integrate both sides.

The Attempt at a Solution


How do I do this? There is no 't' to 'separate' from the equation. Would it just be:
int[1/10n] = int[0t] ?
 
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Hi olicoh! :smile:

You'll need to bring the n and the dn to one side, and the dt to the other side first. Then you'll need to integrate...
 
micromass said:
Hi olicoh! :smile:

You'll need to bring the n and the dn to one side, and the dt to the other side first. Then you'll need to integrate...

So would it be: int[10]dt = int[n]dn?
 
No. That 10 should be 1/10...
 
Is the equation dn/dt= 1/(10n) or dn/dt= (1/10)n ?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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