The differential equation on is given.
Solve the modified homogeneous equation.
What is the general solution to the equation?
Find that particulate solution which goes through T(0,2).
First, I assume you ment .
Anyway, the equation is a first order linear differential equation. In general it can be written down as . Using the variation of the constant method general solution formula can be found, and it goes something like this where is the primitive function of the function , .
Using the formula should suffice to solve the problem(s).