Question

e^t is a solution of ty'' - (2t+1)y' + (t+1)y = 0 what is the general solution

Answer 1

\[y_1=e^t\]
let \(y_2=vy_1\) and find \(v\)

Answer 2

are u familiar with Reduction of Order method?

Answer 3

If you know one solution \(y_1\), you can find the other one by substituting \(y_2 = vy_1\) in the homogenous equation

Answer 4

my v term didnt drop

Answer 5

so tv''e^t + v'e^t + ve^t = 0

Answer 6

that should drop ... equate this term to zero ... your v drops.