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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 2020-1-13

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评论： darova 2020-1-13

采纳的回答： Dimitris Kalogiros

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

I have no clue where this is coming from.

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Bandar 2020-1-13

Use separation variable method in differential equation.

The Legend 2020-1-13

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 2020-1-13

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编辑：Dimitris Kalogiros 2020-1-13

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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The Legend 2020-1-13

You have officially achieved the title of "Legend".

Thank you alot!

darova 2020-1-13

Please accept the answer

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