Results 1 to 6 of 6

Math Help - How to solve dt/dT = -K(T - 5) + H for T?

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    How to solve dt/dT = -K(T - 5) + H for T?

    After flipping it to get dT/dt, how would I solve the integral and rearrange for T? Help appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    Re: How to solve dt/dT = -K(T - 5) + H for T?

    T = \frac{1}{k}  (Ae\textsuperscript{-kt} + 5k + H)

    Is this correct?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    826
    Thanks
    209

    Re: How to solve dt/dT = -K(T - 5) + H for T?

    How we got this. As i understand we get an equation like:
    dt = [ -K(T-5) + H ] dT
    Now integrating we get
    (-K+H) T^2 + 10 T = t
    We have to then solve this quadratic for T.
    Is that correct?

    Quote Originally Posted by iamapineapple View Post
    T = \frac{1}{k}  (Ae\textsuperscript{-kt} + 5k + H)

    Is this correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,407
    Thanks
    1294

    Re: How to solve dt/dT = -K(T - 5) + H for T?

    Quote Originally Posted by iamapineapple View Post
    After flipping it to get dT/dt, how would I solve the integral and rearrange for T? Help appreciated.
    You don't flip the integral at all as your function is already in terms of T. Just integrate both sides.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    Re: How to solve dt/dT = -K(T - 5) + H for T?

    Shoot, sorry, the equation was dT/dt = the equation
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,412
    Thanks
    1328

    Re: How to solve dt/dT = -K(T - 5) + H for T?

    IF the problem was \frac{dt}{dT}= -K(T- 5)+ H then write it as dt= (-K(T- 5)+ H)dT and integrate both sides.

    IF it was \frac{dT}{dt}= -K(T- 5)+ H then write it as \frac{dT}{(T- 5- H/K}= -Kdt and integrate both sides.
    (To integrate on the left, let u= T- 5- H/K.) T will be an exponential of t.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. solve for x
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 11th 2010, 06:18 AM
  2. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 16th 2010, 10:29 PM
  3. Replies: 1
    Last Post: June 9th 2009, 10:37 PM
  4. How do I solve these
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 3rd 2008, 07:52 AM
  5. how to solve for x?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 21st 2008, 10:17 PM

Search Tags


/mathhelpforum @mathhelpforum