GIA'I PHU.O.NG TRNH

103)

Gia'i phu.o.ng trnh:

^y”−2y

⁰

^{+ 5y=xsin 3x}HD gia’i:

Phu.o.ng trnh da.c tru.ng:

^λ

²

^{−2λ+ 5 = 0⇔λ}

¹

^{= 1−2i;λ}

²

^{= 1 + 2i}

NTQ cu'a phu.o.ng trnh thu^an nh^at:

^{y =e}

^x

^(C

1

cos 2x+C

₂

sin 2x)

Do

^±3i

kh^ong pha'i la nghi^e.m cu'a phu.o.ng trnh da.c tru.ng n^en nghi^e.m ri^eng cu'a (2)

du.o..c tm du.o.i da.ng:

^{y= (Ax+B) cos 3x+ (Cx+D) sin 3x}

Thay vao (2) ta du.o..c:

^A= ₂₆^{3 ; B = 57}₂₆^{; C =−}₁₃^{1 ; D= 41}₁₃