How to derive the following equation? I need this for a script that I am working on.
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Equation 1
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261428/image.png)
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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261429/image.png)
Any help is greatly appreciated.
The part that I am most confused about
![eq3.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261433/eq3.png)
I have no clue where this is coming from.
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Accepted Answer
Dimitris Kalogiros
on 13 Jan 2020
Edited: Dimitris Kalogiros
on 13 Jan 2020
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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261440/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261441/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261442/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261443/image.png)
Where, at the last line we merge the two constants into one :
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261444/image.png)
In order to find the value of "const", we set at the last equation t=0. if we define
, we get
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261445/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261446/image.png)
So, at the end of the day, we derive:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/261449/image.png)
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