1.Differential Equation

2. Ordinary Differential EquationODE DNMdbdoow.TWSirhan

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3. Partial Differential EquationD- DE Barnes ldsocgrhksoieoq

ODE I oioudoo.rs :PDE oiobirldoro : Marion 1050

d. UP BAPU

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erooioorooruos Explicit sole

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eooioreriaeeldenw Implicit Sol'

Explicit Sol"

y =fcx)Implicit Sol

"fcxip :c

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s :b,since

a. IN.

unoinoiooiw Initial Valued prob.

- DE ( Sumo its oviduct I- Initial condition cities raining

-Gamo @ insulter (simple equation )

dyd-×

=fax)

y = ffcxldxtc

- Damas beer river separable equation7)handy -

- fgceadx- Bono borrower homogeneous equation

off, = fc2.IT¥¥÷::xo÷i

หรือ

-

① ① O

o

22' 2 3 , (0) 5xy xy x e y= + =

"000- - O

= O O e• ( I

⇐←← ←

= - ⇐÷÷¥.# ⇒ y y = 3×2×2

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 =

-0-0-

-

-

F E

dyDI+ P Y = q

f pdx

y =e- led

" (J get Pd×d× + c)

0010=3 Of =2×23×1pdx =/ 3dx=3X

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"

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]

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

2' cosxy y x x = ( )y =e

- 1×4 = xcosx

p= -iz q - xcosx

Jpdx =/ dx = - lnx

y= e- bd×( Sg .eSPd×d×+c]

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

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

( ) 02

y ='

+ Ytxycotx - x ①¥ Y 't ( itxcotxy

-

- X

--

y't ( It cotx) y -

- I

p = Ixtcotx of =L

jpdxn-fftxtcotxjdx-lnxtlncsinxl-lucxs.int)

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

Jadu = U - v - Svdu= xfcosx) - fC- cosx)dx

= - xcosxtfcosxdx= - Xcosxtsinxtc

Y=×s÷×[- xcosxtsinxtc)y ( Iz ) :O ( X=Iz , y

-

-

o)

°=IIsinIzfEjt te)( = - I

er o b ooo u v o o dry ui n'n onionis

Y = ×s÷ × [- × cos xt s in x - if