To find T you have to take the integral of dT/dt
First divide both sides by -2 to get
dT/dt = -5+2T Then integrate
T = -5T+T^2+C
if T(0) = 2 then
2 = -5(0)+(0)^2+C
therefore, C = 2
Then, T = -5T+T^2 + 2
Now solve for T by subtracting T to the right side
0 = T^2 - 6T + 2 and solving the quadratic equation
I'll use completing the square method:
T^2 - 6T = -2
(T-3)^2 = -2+9 = 7
T-3 = +/-sqrt(7)
T = 3+/-sqrt(7)
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