(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

dT/dt = -k(T - T_m)

T is the temperature of the body,

T_m is the temperature of the surroundings,

-k is some contant

and t is ofcourse time

2. Relevant equations

no idea

3. The attempt at a solution

I tried solving this using first order linear ODE integrating factor method:

so in standard form it can be written as-

T' + kT = T_m

let p(t) = k

then u(t) = exp(∫ k dt)

u(t) = exp(kt) we can forget about the constant.

so multiplying ODE throughout by u(x) :

exp(kt)*(T' + kT) = exp(kt)*(T_m)

integrate both sides

exp(kt)*T = [exp(kt)*(T_m)]/k

divide both sides by u(t)

T = (T_m)/k

my book says this is wrong, why?

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# Solve this ODE (newton's law of cooling)

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