DUNG PHEP D^O'I HAM Y = ZX2 D^E' GIA'I PHU.O.NG TRNH VI PH^AN

160)

Dung phep d^o'i ham

^{y = z}x

²

d^e' gia'i phu.o.ng trnh vi ph^an:

x

²

y” + 4xy

⁰

+ (x

²

+ 2)y=e

^x

HD gia’i: y = zx

²

⇒y

⁰

= z

⁰

x−2zx

³

; y” = z”x

²

−4z

⁰

x+ 6zx

⁴

Phu.o.ng trnh tro.' thanh:

^{z” +z =e}

^x

co m^o.t nghi^e.m ri^eng

^{y= e}₂

^x

Phu.o.ng trnh thu^an nh^at co phu.o.ng trnh da.c tru.ng

^λ

²

^{+ 1 = 0⇔λ=±i}

V^a.y nghi^e.m t^o'ng quat:

^{z =C}

¹

^cosx+C

²

^sinx+e₂

^x

V^a.y

^{y =C}

¹

^cos_x

2

^x +C

₂

sinxx

²

+ e

^x

2x

²