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How to derive the following equation? I need this for a script that I am working on.

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The Legend
The Legend 2020년 1월 13일
댓글: darova 2020년 1월 13일
Equation 1
Can someone help me derive equation (2) from equation (1)?
I have struggled with this for 1 hour and have no clue how to do this.
This is the equation for Newton's Law of Cooling.
Equation 2
Any help is greatly appreciated.
The part that I am most confused about
eq3.png
I have no clue where this is coming from.
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The Legend
The Legend 2020년 1월 13일
Thank you for the reply!
However, I don't see how that will help me reach the bottom equation from the top equation.
The main problem that I am facing is where the ln(T0-Ts) is coming from, I have no clue.

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Dimitris Kalogiros
Dimitris Kalogiros 2020년 1월 13일
편집: Dimitris Kalogiros 2020년 1월 13일
Mr Legend
You question regards your math's homework and not matlab, but I liked your profile's name "the Legend", and I 'll give you an answer
Where, at the last line we merge the two constants into one : .
In order to find the value of "const", we set at the last equation t=0. if we define , we get
So, at the end of the day, we derive:

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