Final answer:
The question involves solving a fourth-order linear differential equation with a non-homogeneous term. The solution requires combining the complementary and particular solutions of the equation.
Step-by-step explanation:
The equation presented, y(4) −2y′′ +y=xe^x, is a differential equation which requires finding a function y that satisfies the equation. Solving such an equation generally involves first finding the complementary solution to the homogeneous part, y(4) −2y′′ +y=0, and then finding a particular solution to the non-homogeneous part, which includes the term xe^x. Since the provided references do not seem directly related or valid for solving this differential equation, they will not be used in the solution process.
Typically, one would solve for the complementary solution using methods such as undetermined coefficients or variation of parameters. Then, for the particular solution, one must guess a function that when plugged into the left side of the original equation, results in the non-homogeneous part. These two solutions are then added together to obtain the general solution to the original differential equation.