111) Gia'i phu.o.ng trnh: y” +y0 =e−x(sinx−cosx)HD gia’i: D - a.t y=e−xz thay vao phu.o.ng trnh du.o..c: z”−z0 = sinx−cosx.Phu.o.ng trnh da.c tru.ng: λ2 −λ = 0⇔λ= 0, λ= 1Nghi^e.m t^o'ng quat: z =C1+C2ex.Tm nghi^e.m ri^eng da.ng: z =Acosx+Bsinx⇒A= 1, B = 0.V^a.y nghi^e.m t^o'ng quat la: y =e−x(C1+C2ex+ cosx)

GIA'I PHU.O.NG TRNH

201-bai-tap-phuong-trinh-vi-phan

111)

^{y” +}^y

⁰

⁼^e

^−x

^(sin^x⁻^cos^x)HD gia’i:

^y⁼^e

^−x

^z”⁻^z

⁰

^{= sin}^x⁻^cos^x.

^λ

⁻^λ ^{= 0}^⇔^λ^{= 0, λ}^{= 1}

^z ⁼^C

⁺^C

^z ⁼^A^cos^x⁺^B^sin^x^⇒^A^{= 1, B} ^{= 0.}

^y ⁼^e

^−x

^(C

⁺^C

^{+ cos}^x)