Question

Draw a direction field for the given differential equation and state whether you think that the solutions for t >0 are converging or diverging. yy(3 ty) - Converge. Diverge Converge for y 20,diverge for y< 0 Converge for y<U, diverge for y 2 0

Answer 1

Here I find solutions of the given differential equation ,as y--------->+ or - infinity then solution of differential equation goes to 0. That is mean by as solution of differential equation converging to 0 as y goes to + or - infinity

And I find direction field for solutions of given differential equation.

-» he given dhffesonlia fquutfon ig ylz y19. 1y) y2. uhtch l6 boemuli's fqualion --). Compaiung abave sq9, wilh DP ohere P- -g en dividinh eq by y,gel pul then du -t du hen eq becomes whith 16 lineae aq?.i9 u + ®U=t du 1-=he- then. hen 1equeited 5ol) ia T tat 니e9t. farS -te 3t - 43 1 1 g4-31+ (-stt g4e but e u then conueeges. -b 1-1 y=o al ( at 1)()ft-try)=-11 lat (i,)z-7 L) =~ thon

dhecton Peld fo Goluton of gien differentfal aqj (Drection et y-axis taxis -2- -3

Plz read carefully and see diagram i.e direction fields