TM NGHI^E.M T^O'NG QUAT CU'A PHU.O.NG TRNH

137)

Tm nghi^e.m t^o'ng quat cu'a phu.o.ng trnh:

^(1−x

²

^)y”−2xy

⁰

^{+ 2y= 0}

khi bi^et m^o.t nghi^e.m ri^eng

^y

¹

^=x.HD gia’i:

Chuy^e'n v^e da.ng

^{y” +p}

¹

^(x)y

⁰

^+p

²

^{(x)y= 0.}

Vo.i

^p

1

(x) = − 2x1−x

²

n^en nghi^e.m

t^o'ng quat cu'a phu.o.ng trnh da~ cho la

R

_2x

Z dxZ

1−x

2

dx

y=x{C

₁

ex

²

(1−x

²

) +C

₂

}x

²

dx+C

₂

} =x{C

₁

=x{(−1x + 12ln1 +x1−x) +C

₂

} =C

₂

x+C

₁

(x2 ln1 +x1−x−1).