Question

2. Solve the following ODEs using an appropriate method. a) (ex + 1) .y = ev sin x b) dy 1 = -y - dx y=x. x > 0 c) (2x2y3 + 3y2) dy = -xy4 dx Cid

Answer 1

@ (@to) de genetsins et 2+1 do = Sinx doc (+3) du = sme dx -] (1+ē3) ds = Jsinydx y-ey=-688C que +68x+S is soliten of 1270 --- This is lineas de diPI=Q P=1 / Q==x Integrating factor is used facta is upar el di वत्र > dx = e inox M=% The general solution is Jous la ldx+c

=-X+ it-jf-dr+c Jidxt.c go) V=-x'4cx is solution of @ © (28344 334) =-334 (234743)* a -474 37443) easy? digte) - dx + ( 2 ) x = 1 =) or one (3)x= This is Berroellige P = 2/4 det u=x² Then du=2x dx from t do y + y = 27 XY xyz

det det I us - 6 This is lineas de P= a=-ber Integrating factor us ellose sing u=74 The solution is 4.6=.f0.14da+C u.J4=yama Paks +C =-657’dyta Uryf = 6 +C u=-etage The solution of is 1x šta