May 1st, 2012, 08:37 PM  #1 
Newbie Joined: Apr 2012 Posts: 18 Thanks: 0  Rate of changes
Think this goes in this forum Speed of sound in air at 0 degrees celsius (or 273 kelvins) is 331.5m/s but speed v increases as the temperature T rises. we know that the rate of change of v in respect to T is (dv/dT) = (331.5) / (2 sqrt(273T) where v is metres and T kelvins. find a formula that expresses v as a function of the temperature (T) how would i do this? thanks 
May 1st, 2012, 10:01 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Rate of changes
We are given the initial value problem: where and . Write the ordinary differential equation as: Now integrate: And we find the general solution: Now, we need to use the initial value to determine the constant of integration, or parameter: And so, the solution satisfying the given condition is: 

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