skan0045

104

17.y" + lfly-l, 1/(0) -1, |l||| - 2 IH. y" 4* y s= 2 cos*, 2/(0) = 0, y'(0) = 1 10. y" + 1/ = sin*, 1/(0) = 1, y'(0) = -1

20.    y" + 9y = sin 3*, 2/(0) = 2, y'(0) = 1

21.    y^/# 4-1/ = 1 4- 2cost, i/(0) = 1, y'(0) = 0

22.    y" - y' = 2(1 -*), y(0) = 1, 2/(0) - 1

23.    y" 4- y' = cos*, 2/(0) = 2, y'(0) = 0

24.    y" -I- 32/fleS 2/(0) = 0, y'(0) = -1

25.    y" - y' = e*cos*, 2/(0) = 0, s/(0) = 0

26.    y'" 4- 2/' == 0,    2/(0) = 0, y'(0) = -1, y"(0) = 2

27.    y'" 4- 2/" = *,    y(0)|f-3, y'(0) = 1, y"(0) = 0

28.    y'" + 32/' = 9t² - 12* 4- 6, 2/(0) = 3, 2/(0) = 0, y"(0) =^^:-4 20. 22/'" + 32/" - 32/ - 22/pe-*, 2/(0) = 0, /(O) 10, y"(0)^l 30.2/'" 4- 2y" -y¹ -2y = sin 3*, 2/(0) = 0, y'(0) = 0, y"(Q) = ,1

31.    i/⁽⁴⁾ - 2/Bo,    3/(0) = Vy'(0') = 0, 2/"(0) == -1,    y'"(0)# 0

32.    y<⁴> -y=t,    y(0) = 0, y'(0) = 0, y"(0)|go, y"'(0)    =    0

33.

34.

2x' — y' - x 4- 2y = 0, x(0) = 1 x' + 3y' - 3x + y — 0, 2/(0) = 0

x' = y— t* 4- 2, ®(0) = 1 y' — a; 4- 3* 4-1, y(0) = 0

•t

35.    y" 4- y' — 42/ — 4 f y(r)dr|^6e* — 4* — 6, 2/(0)    = 0

./o

36.    y (*|—^: 7 cos(* — r)3/(r)dr pssin *

Jo

37.    y(*) 4- / e^<-T2/(r)dr = 2

Jo

38.    y" - 7y 4- 6 [ y(*)dr = 5, y(0) = y'(P)lo

Jo

7.

9.

11.

13.

14.

15. 17.

19.

21.

23.

25.

27.

29.

30.

31.

-(fl* — coh t - nint)

151 1 Ir

-e —e 3    3

6. y = (* 4- 2)e^_4t 3

8. y = — -e^3t sin 2*

= 5*e“^2t

2    §1    _3i / 2    10 _Ł

27 9    \ 27    9

A: i*³ + 2e^-t 4- 2

u

= —*V 12* ⁶

1 m b 1 . „

= MS cos 4* + - sin 4*

16 16 2

Bflif * — ^ sin * — i* cos *

2 2

= 1 + * sin <

1 .    1    l-.A-.-.i

= - sm * — - cos * 4- -e 4-2

Z    Z    Z

1 Es 1 *.

= WB&jĘjjt cos * 4- -e sm *

= i*³ - i*² 4- 2* - 4 - e^-t o l

19

-e 4- —e — -e * 4- -e

2    18    9'

H ml

9

10. y = e ³* ^2 cos 4* 4- ^ sin 4*J

12. y = -1 + * +

13

16.y=^V‘

18. y = *sin* 4-sin*

7    1

20. y = 2cos3*4- — sin3* — -tcosSt 18    6

22. y = e* 4- t²

²⁴-^y=pl⁺f^eSs^e'³‘

26. y = 2 — 2 cos * — sin *

28. y = 3 - 2*² 4- *³

6Ó^e‘ - 20^e~‘ ⁺ l^el| 4^COS3*- k^Shl3t

Odpowiedzi

1. y = -1 + e*

3. y

2. y = -e^2t 4- 2e³* 4. y m -2 4- 5e^a*

= COS *

32. y = — * 4- 7'e* — \e * 4- i sin* 4    4    2

			r 1 5
00 f	X = cos*		\^x=~2^e Eh
1	y = sin *		1 h&Mm
			[y = 2^e +2^e
35. y		| + ie^2t	m 2 , s/3 36. y = "^^e? sin.—*
37. y	-2(l-ć)		38. y = + ie-^3t