Laplace of a Differential Equation

[Fiorella]

I'm trying to solve the problems from this project:

http://www.cengage.com/math/book_content/0495108243_zill/projects_archive/de8e/Project7.pdf"

I already did problem # 1, and now I'm trying to solve problem # 2, which will help me to solve problem # 3.

Solve the differential equation using the Laplace Transform:

http://tinypic.com/r/sq1ait/3"

Knowing that

http://tinypic.com/r/50pkt2/3"


So, what I did was that I plugged in the 2nd equation into the 1st equation, took the Laplace...and I got http://i27.tinypic.com/34glqbq.jpg"


I'm stuck here because I don't know what to do with the T(0) and the S's ...

I appreciate any help, thank you!

 

[HallsofIvy]

One of the things you have written in your solution is "kT= 4.93". Where did you get that from? T is the dependent variable. kT is not a constant.

 

[Fiorella]

Because T = 85 and K = .058. But something that I noticed that I might have wrong is that the time and temperatures are variables, so at a given time the temperature is going to be something, and at another time something else. Thus, I should keep the equations with the variables without plugging in any number so I can have an equation in which to plug in any time and temperature that I want from the table in problem 3.