According to the method of undetermined coefficients, the differential equation y" + 4 y′ + 4y = 3 t² + (t + 2) e−2t will have a particular solution in the form y' ○ Yp = C₁ t² + C₂t + C3 + (C₁t + C5) e−2t Ур Ур = C₁t² + C₂t + C3 + ( C 4 t³ + C 5 t²) e−2t Ур = C₁ t² + C₂ t + С3 + (C4 t + C5) 6 -2t e Ур = C₁t² + (C₂ t² + C3 t) e¯ -2t е Yp = C₁ t² + C₂t + C3 + (C₁ t² + C5 t) e¯ -2t е

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