and use the initial data:
integrate and simplify to obtain
Use the initial data to find C:
To turn this into an equation for the concentration, replace by everywhere that you see it.
when (or where)
The last condition tells you that the inside temperature can have a max or a min only when the the solution curve crosses the graph of . It also tells you that cannot follow exactly (because would have to be zero everywhere along the solution).
For the initial data given starts at 0 and stays strictly below until the curves cross (at some time after when is strictly less than 10). This shows that the amplitude of th inside temperature is smaller than the amplitude of the outside temperature.