Question

solve the following initial value problem

II. Resuelve el problema de valore inicial. -ydx + (x + xy)dy = 0 y(1) = 1

Answer 1

We have, -ydx + (x + xy) dy = 0 or rydrtudy say.dy =0 d x.dy- y.da tray dy = 0 kdy - yon = sary dy OY, rept - Lex say dy 24 212 Or, d ( ) = - ry Чи K dy 3/2 거 leh or, al 1/2) = - Wr. y anom 23/2.7 dy 3/2 у 213/2 d ( 2 ) = - ( ydy 13/2 Y Now, integrating both sides / gel- (1/2) 3/2 dy Y -3/2 vo 2/4) اما
The answer sheet has three pages.it is the first page
= - lnly) + 9 2 where an integrating constant Janda = pent and nti dr In(all te 거 -1/2 je - enly I to -1/2 -1/2 OY. = -lollte 2 07-22 en 1+0 V = 14 / an -Poly Itc -2. a or - 2. - Infylte Y Condition, y(1) = 1 By the given ee. when x= 1, Then 7=1 This from o we get = -ln (1) + c [since, ln (1) = 0 - 2 = 0 + c
second page
c = -2 we get Petting the value of c=-2 in ① -2.5 7 = -lo/11 - 2 Or, 2. √ √ = enly) +2 Therefore, the solection of the given diff. ecreation is 2J 7/7 = ental + 2
Third/last page