ay t cD inv - Suranaree University of Technology
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Transcript of ay t cD inv - Suranaree University of Technology
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t pony'+ quay = cD ( ios inv )
1 .
r Cx) IO
y"t p Cx) y
'
t g Cx) y = O
GAM 86 onWhoo!homogeneous equation
2 .r Cx) fo
y"t p ca y
't qcxly ircxl
Gw mot si conatusnonhomogeneous equation
ay"t by 't Cy = 0
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x =- b t TEC-
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'' 2 ' 15 0y y y+ =เมือทราบว่าผลเฉลยหนึงของสมการคือ 3
1( ) xy x e=-
--
promotor 22+2×-15=0( X - 3) (Xt5)=0
7=3,-5
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erooaoooevnioehl y=qe3×tqe5×i. y''
try'- 15 y =0
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2
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= e' ''JE" -6×d×=e"fI8×d×
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= e. e- = e- = e-- 8 -8 - 8
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y = E. Y,tail,
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+ EE"( E=cIg )
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rap y'+ pi y =o
GomgbooI 22 - 2 Lp X t p
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( 2X -pi =od X -B =O
2 X = 13
¥ = e£×' ' By
42 = Y, 1¥
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⑧y"-
rap y'+ pi y =oT
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Yz =xet⇐
เมือทราบว่าผลเฉลยหนึงของสมการคือ 1( )y x x=O
=
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= Y, ¥, IPad'd×
I dx
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y = x f x- 3 dx
'
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x
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2 '' 4 ' 6 0, 0x y xy y x + = เมือทราบว่าผลเฉลยหนึงของสมการคือ 2
1( )y x x=O€7-
- Y, ffy
,,e- Had×d×
a = XZ b =-4 X
Y,= x' I ¥, e-
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'
= x' f Ia e dx
4 f IdxY,
'
= x' f Ia e dx
a lnx=×' f I e d xx 4
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f Ia - e dx
= 5,1¥ . ¥gd× = x' ft dx
= X . x = X
¥-
- G Y, t Cz Ya = C.
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22 '' 3 ' 0, 0x y xy y x+ =
เมือทราบว่าผลเฉลยหนึงของสมการคือ 11( )y xx
=
O O
Y.
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, I fy,pe-' Id'd×
A = 2×2,b = 3 x
Ye = ⇐ , 1¥,et dx
dx
Ye = ⇐ , 1¥,et dx
dx
= I f x2e
' III dxdx
= I 1 x? e- I
en xdx
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- Z d x = I f x" Id
x
x
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Y = C. Y,
+ Czyz
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2 '' 5 ' 9 0, 0x y xy y x + =
เมือทราบว่าผลเฉลยหนึงของสมการคือ 31( )y x x=
000
a -
- x' b = -5 x
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= x3 / x-6.e5l" "d ×
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= C,X't Cz x3 lnlx I
ay"
+ by 't Cy =Oa,b,c eiwoinysoio
Gums bow ax't bat c=o
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XXb.2- aac :O
, y = C. e'''
teexeb'- aac -10
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y : er×[ qcoscsxltqsincs xD
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Ye.
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y = C, Y,t Ce Ya
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Duero bare violates Romo loading
แบบฝึกหัด
จงหาผลเฉลยของสมการ หรือ ปัญหาค่าตังต้นต่อไปนี
'' 2 ' 4 0, (0) 2, '(0) 6y y y y y+ + = = =2 2'' ' 0, ( ) , '( )y ey e y y e e y e e+ + = = =
2 1 1'' 0, ( ) , '( ) 12 2
y y y y + = = =
22 '' 3 ' 0, 0x y xy y x+ =
เมือทราบว่าผลเฉลยหนึงของสมการคือ 11( )y xx
=
