Scan10032

o

e^x

e^x +1

W

W₂(x) =

Wi(x) = \

⁰

e^x I e^x + l

-1 Ąg*

\e^x + !==€ dx = di \e^x =/-li

1    r di

2

^J ^-1)

dt =

c₂w=4j

ij—*+-f

2 >t lh

h8

dx =!

dt 1. . ,    ,

2 ^J e +1

| e^xdx = dt\

■^ii+c'4H7y

1 rt +1-1

C,

i t tdt i et +1 -1 * i f. - -= — -dtm— \dt

Emm ? !

f + 1

r + 1

2 ^Jć+1

■dt

20

1 1, ,		1 ,
m—t +—in \t	+11+C2 — —	—e
2 2		2
Ostatecznie: m		+ C
PRZYKŁAD

JjHB

•1|+C₂

- In|e^x +

c₂y-

i. /'+>> = tg²x

i. y^+y = o

. a = 0-,

mmkmd Bi mmmm

,y_0/ = Cj cosor+C₂ sin x

II. 7 = C₁(x)cosx + C^inx J C₁'(x)cosx+ C₂'(x)sinx = O C₁'(x) sin x + C₂'(x) cosx = tg²x

2 r