Substitute this int the differential Equation: y" - 8y = 16x2 (6 Ax + 2B) – 8 (Ax² + Bx +c) = 16m² Equating coefficients of like terms: - 8A2 + (64-88) x + (28-8c)=16x2 Equating Coefficients: -8A = 16 =) A = −2 6A -8B0 =) - 12-8B = 0 =) 6 = -12 = -3/2 So the particular Solution is: 3. Geneal Jp(x) = – 2x – 3/2 × Solution Sum of Solutions. IS Κ -3/8 If the homogeneous and particle general solution y(x) = Y₁ (x) + Yp(x) →) y(x) = Ce² + 2 x cos (√34) + Cze din √3x) 2x² -¾½ x – 38.