Final answer:
To find the particular solution of the differential equation y" - 5y' + 4y = 8eˣ, use the method of undetermined coefficients with the guess of A*eˣ. Solve for A to find the particular solution y = 8eˣ.
Step-by-step explanation:
To find the particular solution of the differential equation y" - 5y' + 4y = 8eˣ, we can use the method of undetermined coefficients. Since 8eˣ is an exponential function, we can guess that the particular solution has the form A*eˣ, where A is a constant to be determined.
Substituting A*eˣ into the differential equation, we get (A - 5A + 4A)*eˣ = 8eˣ. Simplifying, we have A*eˣ = 8eˣ, which implies A = 8.
Therefore, the particular solution of the differential equation is y = 8eˣ.