Solution to Diff Eq question

Question

1g. Find all of the solutions of the given differential equation: y'=-e^^2t+4y

Answer 1

y' = -e^2t· e^4y; e^{- 4y}dy = - e^2tdt; ∫e^-4ydy = - ∫e^2tdt; - e^-4y/4 = - e^2t/2 - C/4; e^-4y = 2e^2t + C