skan0023

p

p

8. j/-' + 7y^r + Zy ^{68 0} 10.2/" - 2/ - 62/ = ⁰ 12. 2y" -52/' = ⁰ 14.2/" - 6/ + 93/ = ⁰ 16. y" - 102/' + 252/ = ° 18. 42/" - 4y⁷ + 3/ = ⁰ 20. 8y" + 2y' - 2/ * ⁰

22.2/" + 2/ + i°y ' ⁰

24. 22/" + 2y‘ + 2/ = ° 26. 2/'" + Zy" - *y = ⁰ 28. y"¹ + y’ = O 30.2/^JV + y" = 0 32.2/^ZV - 3/ = O

* y' - Qy » O \/d)y" — 3J/' -ł-    = O

W) / = O

\mzv" + y = 0

ĄQv" + jflf + 1% = o

©2/" + V + 42/ = 0

S2J/" -5y' + 2y = O y" — 4y' + 5y — O y" + 10y' + 29j/ = O \lfi5) y'" + y" ~2y' = O '$7) y"¹ + Zy" = O &My^IV -2y" + y = 0

+ 2 y"¹ + Zy" = O \fl3; y^IV + 3y'" + Zy" + y' = O

Wyznaczyć całki szczególne następujących zagadnień początkowych:

■ - Zy' - 42/ = O, 2/(0) = 1, 2/'(0) = 2 2/" ₇J/ = O, 2/(0) = O, 2/'(0)j|l 2/" - 22/^; + 2y = O, 2/(0) = 1, 2/'(0) = O IZ&y"- W +132/ = O, 2/(0) = -1, 2/'(0) = 2 \J39. r - 3/' | O, 2/(0) = 3, 2/'(0) = -1, 2/"(0) = 1 (4& y^IV - V = O, 2/(0) = 2/'(0) = 2/"(0) = O, 2/"^,(0) = 1 i    + y = °» 2/(0) = O, 2/^;(0) = 1

Wyznaczyć całki ogólne liniowych równań niejednorodnych:

43. 2/" ' ^l°y'+ 252/ = 30® + 3

45.2/" -y' =g-3

47.2/" -3/⁷ “ ²2/ = 8e^ _sJ.

49.2/" " 2y⁷ + 2/ =

51. y" + 82/ + 362/ * 72 cos 6® 53.2/" + 42/ = 3 sin 2;i;

(42Cy' + Zy' + 2y = 6

\4& y"-7y'+I2y = 12®²+10®-ll

Sg 2/" -72/' + 102/ = 246*

- 52/' + 42/ = 86*

I Sb. 2/" - 32/' + 2y = sin a:

1 .

(52. y" -1/ = -x cos2®

M,	fi 4	1(1// ■» 24 gos 4®
1 Uli.	V *	■ 2v' Hf* 6®<s®
fili;	.dl V "	* w ■ Sc^10 sin x
00,'	iw" 4	* U ■> 2® sin x
oa,	1/"-	• y m &^tt sin 2®
j }4j	v" ■	y sin x cos x
no,	w"-	- 2y' — 3j/ — 4® — 5 + 6®e^2*
ON.	1/"-	■6?/ + 93/ = 6®^2 + 2-12e^3*/
TO.	p	+ 4y' = 24®^2 + 8® + 4
Tli.	W'"	+ 8y » 20e® sin ®
^1 T4<	I/'^1'	+ 2y” + 2/ = (® - l)^2*
TO.	V^vl	•\-9y^rv = sin 2® —cos 2®+4
ffw.	y-	f 32/' + 2y = sine*'
NO.	'V ■
N<i.	p	- 2y' + y = e*arctg®
N4<	, I/"
NO.	1W	- 4y' + 3y = (1 + e^-*')^--
NN	w	1 + W =
		cos®
00	Igjp	+ 23/ + y = 3e^-*\/® + l;,/
00	• w"	H 4?/ = -........
		sin 2®
04.	ii/"-	f 4j/'+4y = e'"^2®(4®^3+®)^-1
(au	Ju"	- 43/' + 4y ss ®"^12e^2* ln®
ON	•V	1 + 3/ = _a li'
100	.w"	- y' = e“^a® cose“®

55. 3/"+ 3/= 4®+ 10 sin®

57. y" - 5y' + 4y- 4®²e²*

59. y'' - 9y = e³® cos®

61. y" - 2y' + 5y = e* cos 2x 63. y" + y = — 2 sin x + 4® cos a:

,^77^ ¹

\($j)y'' - y + ^ = 3 + ef #

— 4y' + 4y = 2e²* +4x - 12 o y'" + 2y" + 2/'=5+2(sin ®-fcos x) © (js)y^,n - 3y" + Sy'-y ^,x - 4e* ^ & J 75. y^IV - y” = 4® +2®e^-*. iJBlS - y'" = xe^x';.

79. y" + 23/ + 3/ ■■p=.&^r* In ą: ;

83. y" Bil =?4—

- cos®

+ sy + 2^--^

87. y" + y=^—

sina; • -

89. 3/" + 43/ = 2^g®

91. y" - y = e~^x sine^-* + cose"*

H BĘlfSB ’

93. 3/"-63/+ 9,3/ = ^2-

95. y” - IO3/' + 25y = e⁵* ln x

97. y" + 23/' + y_t = 4e^-*®^-1(ln a;)²

I (jOlJy'" + 3/' = tg² a;