For intervals of validity for a first order, linear differential equation, how does the interval of validity change if the equation y'+p(t)y=g(t) versus y'+p(t)y=0? Does it make the interval dependent on g(t) in the first one? What if the two solutions to the equations were added, how would you explain the outcome solution to also be a solution to y'+p(t)y=g(t) as well?

Question

anonymous · Answer

The last question is what I am trying to prove. The first part is my attempt at arriving at a proof.