I'm at a loss on ones like this problem. I'm working on a reduction of order problem and have come across the equation v''t+v'=0.
I have the solution manual to the book the problem is from, and it says that solving for v', I should get v'(t)=ct^{-1}, which can be integrated to get $v(t)=c_1*\ln(t)+c_2$.
I cannot for the life of me figure out the method of going from v''t+v'=0 to v'(t)=ct^{-1}. What is the method I should use and what are the steps?