#### codproplayd

##### New member

- Joined
- Oct 31, 2019

- Messages
- 2

I know that to integrate Newton's law of cooling's differential equation

**T′(t)=k(T(t)−A)**

*where T=temperature, t=time, A=constant temperature of the surrounding, and k is constant*, I can use Laplace transform:

**T′(t)=K⋅(T(t)−A)→s⋅T(s)−T(0)=K⋅(T(s)−A⋅1/s)**

Then solve for T (s) and use the inverse transform.

**T(s)=(T(0)−K⋅A⋅(1/s))/(s−K) => T(t)=A+e^Kt(T(0)−A)**correct me if I am mistaken please

And from there I could solve the equation, which is easy, but I don't know the step-by-step method of using both the Laplace transform and inverse with adding the integrals to clearly explain what I did on paper.

I would be thankful if someone would help me out with this one