2. Ordinary Equation ODE DNMdbdoow.TWSirhanjessada/Metal/First-Order-ODE... · 2020. 3. 18. ·...
Transcript of 2. Ordinary Equation ODE DNMdbdoow.TWSirhanjessada/Metal/First-Order-ODE... · 2020. 3. 18. ·...
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1.Differential Equation
2. Ordinary Differential EquationODE DNMdbdoow.TWSirhan
.
3. Partial Differential EquationD- DE Barnes ldsocgrhksoieoq
ODE I oioudoo.rs :PDE oiobirldoro : Marion 1050
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d. UP BAPU
5.
erooioorooruos Explicit sole
6.
eooioreriaeeldenw Implicit Sol'
Explicit Sol"
y =fcx)Implicit Sol
"fcxip :c
> . erotomania General Sol 'coin C )
8 .evolution 6am : Particular 501
"
s :b,since
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a. IN.
unoinoiooiw Initial Valued prob.
- DE ( Sumo its oviduct I- Initial condition cities raining
-Gamo @ insulter (simple equation )
dyd-×
=fax)
y = ffcxldxtc
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- Damas beer river separable equation7)handy -
- fgceadx- Bono borrower homogeneous equation
off, = fc2.IT¥¥÷::xo÷i
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หรือ
-
① ① O
o
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22' 2 3 , (0) 5xy xy x e y= + =
"000- - O
= O O e• ( I
⇐←← ←
= - ⇐÷÷¥.# ⇒ y y = 3×2×2
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dyd-×t PLAY = qcx )
etpcxidxfddyxtpcxy) . elp"'d×qc×,
ey×+eSPd¥y= e'P'"
d×qc× ,
ddzfespdxyy.ae/Pcx1dxgdeodx.y=JelPd+gdx+c①e-fpdxfgesedf.de tfy =
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-0-0-
-
-
F E
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dyDI+ P Y = q
f pdx
y =e- led
" (J get Pd×d× + c)
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0010=3 Of =2×23×1pdx =/ 3dx=3X
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P =3 Of = 2xe-I
J pdx = / s d x = 3X
y = e- S Rdx [ fq.es "did x t C)
y = e'3×1 ) ex d x t c)= e-3×1 J 2x d x t c)= e-" [ *¥'t of = e-
" ( x'to]
y = e-37 x' ice"
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2
2 6 xdy xy xedx
=2
p = - 2x of = 6 xet
j pdx = f C-2Nd x = - X'
y = e-led×[ f q .
et Pd×d× +c)y = e-"" ( I 6xe¥dx to]
= e" [ I 6 xdx t c]
= e" [* If + is a e
"Csx'tc]
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x' y'- 3 Xy =2④
Isis 's sumo 6dm Ew+2 y
'= 2 y't 3×4
y'= aat'II
= 41×5+3 (¥ ) bumsV -
- I'On artist
x
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2' cosxy y x x = ( )y =e
- 1×4 = xcosx
p= -iz q - xcosx
Jpdx =/ dx = - lnx
y= e- bd×( Sg .eSPd×d×+c]
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J pdx =/ dx = - In x
y = e- Tedx ( Sg.ex to]e-spdx . e-
thnx! een ×efpdx = e-
lux= eh G-
'
l=x
- '
= Ix
y = x ( fx-cosx.tn#dx + c)= x ( J cos xdx to]=x ( sin x +c) = X - sin x tic
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y = x ( sin x to] = X - sin x + *c
oth y CIT)- IT ( x -- IT , y
.- IT )
IT = IT sit + c)c = It = '
y = x [ sin x ti )b disease rooster anoints
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( ) 02
y ='
+ Ytxycotx - x ①¥ Y 't ( itxcotxy
-
- X
--
y't ( It cotx) y -
- I
p = Ixtcotx of =L
jpdxn-fftxtcotxjdx-lnxtlncsinxl-lucxs.int)
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y = et Pdx [ Iq . esedxdx +c)= e-lncx.sinxlfgz.edu" - sing! + c)=elnccxsinxl'll fxsinxdxtc]
= x.si, [ fxsinxdxtc]
Jxsinxdx Put u :X du : sinxdx
du =dx V -
-- cos ×
Jadu = U - v - Sv du= x C- cos x) - IC- cosx) dx
= - xcosx + fcosxdx
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Jadu = U - v - Svdu= xfcosx) - fC- cosx)dx
= - xcosxtfcosxdx= - Xcosxtsinxtc
Y=×s÷×[- xcosxtsinxtc)y ( Iz ) :O ( X=Iz , y
-
-
o)
°=IIsinIzfEjt te)( = - I
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er o b ooo u v o o dry ui n'n onionis
Y = ×s÷ × [- × cos xt s in x - if