Question

Question 2: (40 marks) Find the general solution of the differential equation y" - 3y' – 4y = Sin(t) by using the method of undetermined coefficients.

differential lesson

Answer 1

Salection@:- Cylreg differential equation is you: = 39"-4y= = sin lt (jf Auxilary equation of equation (J 18 m2 -3m-450 > m-4) (n+1) to If my and m₂ are two real distinct root then miz C.FI Ae Either. OR A Bemu, m-450 mt=0 L..m=4 2) ܚܐ

Therefore complementary function (Cf) = ne* +8244 Noco Presticular integral (PIJ) 1 Sirit) D2 - 3D-4 1 SAM) -412_30-4 Sinit) -3D-5 -3045 sint 630+5) (205) E30+5) 90²_25 sint) +3045) SMA 9(-32)-25 - 1 1-30+5) sint 34 = 3 o sint) -s sint) 34 34 por = 3 34 cosity 5 sint) 34 Therefore generals solution is YH) = e.Ftp.I -t :y (H) = Ae tBe At t 3 caslt) - Sint 34 34 Opower