GIA'I PHU.O.NG TRNH

35)

Gia'i phu.o.ng trnh:

^{y” cosy+ (y}

⁰

⁾

²

^siny=y

⁰

HD gia’i: y =C :

hang la m^o.t nghi^e.m.

y6=C

(hang). D - a.t

^y

⁰

^{=p⇒y” =pdp}_dy

(ham theo

^y

)

thay vao (2):

^dpdycosy+psiny= 1

: phu.o.ng trnh tuy^en tnh.

Phu.o.ng trnh thu^an nh^at co nghi^e.m t^o'ng quat:

^p=Ccosy.

bi^en thi^en hang s^o du.o..c

^C=

tg

^y

+

^C

1

.

tu. do

^{p= dy}dx = siny+C

₁

cosy⇔ dysiny+C

₁

cosy =dxrtgy1 + 1C

₁

2 +C

₁

²

− 1

tch ph^an di d^en:

p ¹=x+C

₂

C

₁

²

+ 1ln−tgyC

₁

²

+ 12+