Golden Differential Equations by N.P. Bali

By N.P. Bali

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Example text

Iqrv _ _ Iog:r+c " , - - +Iog - _ _ 1ogr+c 2y' r " • .. Ioc J' ... ill the required IOluUon. pIe So SoWc tM. ,. d,. do • (iih',rdr _ (r' .. rJd;y .. _m ... ;: - ",,' -u' ,,' "I d. " "WI -- ... So . plltatina the WI '7 .. - -; . ,_ du vanIO~ IntegraUna' both 1Ii"-. ;. the reqnind IOluI;on. ,tben ... t:~. ' +11',,' - I .. t. -'_ . _do" 01" ( +;I)d.. __ -:;-do " .... , - ~ .. lor II .. - lor " .. c " " "" - - I + .. l"-kIc ,,·t , " +loc,. -Q " - - 10&" +c - i7 . dlGlution. ---. t '" . 2l ,+~ " ...

Dogr .. -. Jogcr3 ;«xl .. 3yi) .. o the d, (iu) Given equation ill ~uired ""[,,lion. , ... (i ) dx " X'+yl Put y" "" then dy du dx " ,,+x rlx :. dv " +r. dx .. ,,2 Fmm (i), ,,'+3,)" c -. -, - _ . ' or cW "",2 " ",,·x· . '. \og" .. -log% .. c -h , . Iqrv _ _ Iog:r+c " , - - +Iog - _ _ 1ogr+c 2y' r " • .. Ioc J' ... ill the required IOluUon. pIe So SoWc tM. ,. d,. do • (iih',rdr _ (r' .. rJd;y .. _m ... ;: - ",,' -u' ,,' "I d. " "WI -- ... So . plltatina the WI '7 .. - -; . ,_ du vanIO~ IntegraUna' both 1Ii"-.

R Ute required N I"tion. (1-"'1 y dy. :l ydy. 3<""1nnydr ,.. , y dy. " " "wll;cll i. 3 Jog ('" _ 1) + e, log ttlny"' log (... - 1' + log c log tany • loge (... ,I"tion. En mpl .. 3. : (j) (r _yr) dy .. O (m(x - r~h -(y - ryj dy. O. Sol. (i) (.... - yx') dy .. (y" .. xy") h • 0 rr .. x"(1-y)dy +r(l +x)dx. , l+x Y +7 dr • 0 .. ).... ) y ' y '" (...!. , .. Iogx . )•~ I. the reqd .... , " u-rx )h-{Jo - ryl dy_O log ! _ (1. r)h I"lion. rrating both aidH. )1 dJ: .. --1) --,u+c, -" - - 2 "" " 1- , l-r 2 -jlctlt -r).

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