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Solution: For a linear differential equation with a polynomial non-homogeneous term of degree 1 (i.e., f(x) = 26x + 8), assume a general linear particular solution: y_p(x) = Ax + B Compute the first and second derivatives of y_p(x): y_p'(x) = A y_p''(x) = 0 Substitute y_p(x), y_p'(x), and y_p''(x) into the differential equation: 0 + 4(A) + 13(Ax + B) = 26x + 8 13Ax + (4A + 13B) = 26x + 8 Equate coefficients of corresponding powers of x: For x¹: 13A = 26 ⟹ A = 2 For x⁰: 4A + 13B = 8 4(2) + 13B = 8 ⟹ 8 + 13B = 8 ⟹ 13B = 0 ⟹ B = 0 Construct the final particular solution: y_p(x) = 2x