Solving Differential Equations to 2 ln |20-2h| = kt + c

kyu
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-2 ln |20-2h| = kt + c

kinda lost. solving (i) would be enough for me
 

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kyu said:

Homework Statement


Homework Equations


The Attempt at a Solution



-2 ln |20-2h| = kt + c

kinda lost. solving (i) would be enough for me

The first part of the question is asking you to solve the separable differential equation. It looks like your solution is fine to me. Except you need to re-arrange it a bit. Solve for ##h(t)##.

The second part of the question is 'hinting' at an initial condition. In particular: ##h(5) = 2##. So what does that tell you about the rest of the information?
 
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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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