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## Main Question or Discussion Point

I have a book called REA 's problem solvers: Differential Equations Year 2004 and the problem 12-14 on page 244 might have problems with it and I want to ask to see if anyone else thinks so.

The problem is basically Newton's cooling where they ask to find

T - T_o = (T_i - T_o) e^(-kt) (1)

where T_i = T when t = 0.

Given dT/dt = -k(T - T_o) (2)

where T_o is the temperature of the surrounding medium.

The part that seems incorrect to me is where they integrate after rearranging (2) to get

LN(T - T_o) = -kt + LN(C)

1. Shouldn't the left side be -LN(T_o - T) after integration?

2. How do they get LN(C) instead of just C and then solving for t = 0, C = -LN(T_o - T)?

The problem is basically Newton's cooling where they ask to find

T - T_o = (T_i - T_o) e^(-kt) (1)

where T_i = T when t = 0.

Given dT/dt = -k(T - T_o) (2)

where T_o is the temperature of the surrounding medium.

The part that seems incorrect to me is where they integrate after rearranging (2) to get

LN(T - T_o) = -kt + LN(C)

1. Shouldn't the left side be -LN(T_o - T) after integration?

2. How do they get LN(C) instead of just C and then solving for t = 0, C = -LN(T_o - T)?