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

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.

[Bandar]

Use separation variable method in differential equation.

[The Legend]

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.

Answer 1

[Dimitris Kalogiros]

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:

[The Legend]

You have officially achieved the title of "Legend".

Thank you alot!

[darova]

Please accept the answer