Problem 15. Find the general solutions of the following linear ODES. (1) g" +3y + 2y...

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Answer 1

Answer #1

1) given Y + 3y + 2y = cost - (+ 3D + 2) y - Cose, Defa This is of the form of f(Dy=a f(o)= 8+30+2, Q = cost Auxiliary equat 1

Cosa 1-3D (1+30) (1-3D) (- 3D) cosa Yp 2 (1-3D) Cosx 1-9(-12) cosx-3D [cosx) 1 +9 Yp Cosa + 3 sina general solution is Y=Y+Yp 2

Auxiliary equation is flm)_o 13 - 0 m- - 1 0 1 - (m-1) (m²+m+o)=0 m=1 m² + mrla m= -lt Si-a 2 ma -13 2 ma! - 2 + 3 2 Compleme 3

pesticular solution is Sp: to a -Sp- Sind Sina Ip = D²D-1 sina 20-1 sina D-1 sinx sina - (D-1) (D+1) (0-1) -(0-1) D-1 (6.1) S 4

If you satisfy with my answer please give?

Answer 2

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