TM NGHI^E.M T^O'NG QUAT CU'A PHU.O.NG TRNH X2Y”−2XY0−4Y= 0,KHI BI...

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

^x

²

^y”−2xy

⁰

^{−4y= 0,}

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

^y

¹

^{= 1}_x

.

HD gia’i: y

1

= 1x

la m^o.t nghi^e.m cu'a phu.o.ng trnh. Ta tm nghi^e.m ri^eng

^y

²

^=u(x)1_x^.

Thay vao phu.o.ng trnh ta tm du.o..c

^y

²

^=x

⁴

^.

V^a.y nghi^e.m t^o'ng quat cu'a phu.o.ng trnh

la

y= C

₁

x +C

2

x

⁴

.