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H D tf fo sontial Jayoshich Saha Panaclions . 2. % Dtffere mitat Equation? An. equo-li sw gmvolving re — Gn clo pen chet yoriabte, deperncte rt aact ho AI 2 eeatiok coo fici cats at the Aopen cterrt vaviabss , % Ovehar BK Degoce of Differenttat Bae? ‘The, orcters ak the hig hast cif ferentiot coc ffictent appearing wm the aif berentHatl equ” Lt ws Caltech orckr a, Aifperenrttat aqult, “The exporant of the hig Rest lif fescn-Hal eocffictemt , when the cBfbarertfat oyu SO ™m att th oljbere mat coxfficient’, ole gues © b athe Ae bheventt ot ely romiat fs known as thy OV rati ow . 4 Pormattow of Diffewen-ftat Eqirations : a) Difjeremitecte the i equ ™ wort. the qm de-ponadent varia bAc as momy tmes as the number ot ar brloay couctamts wm tt. b) Eltminete dhe arbilary contonts. he ol} boven Hat oq ri th K The order of, wm le pencdtent be oquat -to num ber oF anck not 2Yyerat to the Aorramet erg of akt the parameters UM the nium loan family of Carve, k Golut®ow of o AU bperemtt at equ” 4 a) A qenarat. Gol” or an votegrat: A wekattow betwee wv He VOTR Oo LoS Crot om val Wingy the cerdy atives) whtok Cow tains he Same nember af anbi-tasy Constants as the oroler al oyuarttov. , b) Pawitoutar Soluttow oF -port?cutor Varlegror: Oblatned from ths qemerot Soluto ow by assig ni 74 parttortar yolucs +o the oabttory constant Tm phe dina solutfow , & Def. ons” of 19+ Oroler - yet Degree! B= FY), which athe vartabtes awe bd Equations Ya) Seperabts tf gy = Fey) oan be 2rpaessect qn the form Fa) ta = gCydoly » By tarlegrattny sthes, Soltet for — Ji@jdz = away +e. © Roducibte +o the sepayabte variate dybe 3 a = FC ox+ iy aa) Bs Solved ke petting Oatby +@ = Bet * Stone geneous Lf equ Ye(ny)dx +Q Gaypoay= 0 os catted home — geneous tf PRA ow home geneous Lunchtens oh the Som oleg Tea am x AY. Reolucibke + y= $(%) y Sebstttucte yexu ,u is ankmn own function , The. oy as Amie fowmect to an sap wity Vvartabte geparorks , i) ae i ant by ter b, = eceprt , Ob, — Agb #0. w=uth, y = utk Wo . then Sebstttute TH AQybo- Gob, =O , Kw a,x by. trans bovme grt a vartobte sepotobte 4 POY) funcdtow Ts homog cheous ok oleg ree n, of for any aeat+ , P tu ty) = 4” (Plmy)). ” ¢ y) ¢ J Joyoshish Saha form . mdy - yds dan tt Ay ~ peri a . d CZ) » d (io i) me cae {4 Yo La (Ay A Ax yda-ady i A[ Im (ay) ] = a it, dfn »(%)l= ee 19 d \n Vie 7] aay ayes 13, d Jylacary’) aoe) a la: [scopy] = 252 14) a (- fay) = = ia 4 (F ues alas eVAXx \ oy at 1) d(% =) ° y- 1p A(R Ny ae ne eee | 19) dt fey? _ fey pew (0-92) LR ye veme, 4 = Wu) maAy-yax = Ab %) aAa+ y ay = 7lr ~% ty y KISH Oyler bemear Atk. syn: AY 5 Pe) -y = AC) S PAK Solute * yer | ge aw JPA". Tp = Srlagvating — artr. Days oy” dividing ™ —+ yy Py Me 8. ty Die i Cot gE = oo OQ Gh4 (omype = (1g. ac n)P An £. ne 4 Waornoulli’s bqus 5 SF = Qolustow ts (Inn) Pax aod Pax f SUK) g. ot y An. Sayoshich Saha Def fosen-or Equattons. 9 t “Orthogonal So afeetowy : tiny curve, | which cuts alle momber of vu qe pomtly ok Guaves ad wig hs angts, - aatted an orthe gonot rhroje ctory of the jams ly, Y \Papencliee for kineou OT ° 5) Lox f @y 9 =O 6s the LYLo AT ow ak fant y. S) Dieren ite fre , wrt «©. ® ettminata2 Cc. th tH) Substttate - ee for pat That fy ° ash, eye oh OT. Yaw, solve BE to get OT. Sayochich Saha 
