Final answer:
To solve the given differential equation by undetermined coefficients, assume the solution has the form y = Ax² + Bxeˣ and substitute it into the equation to find the values of A and B.
Step-by-step explanation:
The given differential equation is y'' - 8y' + 20y = 200x² - 65xeˣ.
To solve this differential equation by undetermined coefficients, we assume the solution has the form y = Ax² + Bxeˣ, where A and B are constants. We then substitute this assumed solution into the differential equation and solve for A and B.
After solving, we find that A = 0.1 and B = -0.125.