I am trying to use Mathematica to solve a relatively simple ODE involving parameter(s). I would like to use a set of conditions to solve for the particular solution of the ODE. I understand how to make Mathematica find values for the constants that arise during the process of solving the ODE, but what about solving for constants/coefficients already present in the original ODE? Here is a simple example involving Newton's Law of Cooling...
Here is the code I tried:
DSolve[
{
T'[t] == -k*(T[t] - Ta),
T[0] == 70,
T[1/2] == 110,
T[1] == 145
},
{T[t], t, k},
{t}
]
I feel like I need a two step process... first solve the ODE with the parameters, and then solve for the parameters afterwards. I'm just not sure where to start.
Thank you in advance!