Newton Law - Cooling of a Cake

syms T(t) k  

Tm=70;

f = diff(T) == k * (T-Tm)
dsolve(f)

%FIND K
T = dsolve(f, T(0)==300)
k = dsolve(T,T(3)==200)
%I want to apply t=3 and T=200 at the T formula to find the k value and
%then I need insert the k value in the T formula to get my final answer

Answer 1

[Torsten]

syms T(t) Tm k
eqn = diff(T,t)==k*(T-Tm)
T = dsolve(eqn)
vars = symvar(T);
C1 = vars(1);
T = subs(T,Tm,70)
eqn1 = subs(T,t,0)==300
eqn2 = subs(T,t,3)==200
sol = solve([eqn1,eqn2])
T = subs(T,[k,C1],[sol.k,sol.C1])

[Adrielli]

That's exactly what I needed, thank you so much!