The function Ce^(-5t)+e^2 solves the differential equation y"+6y'=-5y+5e^2 true or false

Answer 1

y = Ce^-5t + e²

y' = -5Ce^-5t

y" = 25Ce^-5t

y" + 6y' = 25Ce^-5t - 30Ce^-5t = -5Ce^-5t

-5y + 5e² = -5(Ce^-5t + e²) + 5e² = -5Ce^-5t

Since y = Ce^-5t + e² satisfies the given differential equation, y = Ce^-5t + e² is a solution.