Final answer:
To solve the given differential equation y" + 4y = cos²(x) by undetermined coefficients, assume a particular solution in the form of a polynomial and solve for the constants.
Step-by-step explanation:
To solve the given differential equation y" + 4y = cos²(x) by undetermined coefficients, we assume a particular solution in the form of a polynomial. Since the right-hand side is cos²(x), we assume a particular solution of the form Ax² + Bx + C. Substituting this into the differential equation and equating coefficients, we can solve for the constants A, B, and C. Finally, the general solution to the differential equation will be the sum of the homogeneous solution and the particular solution.