Question

Solve the Bernoulli equation for y. dy 5y + yº. dt Use the following initial condition: y(0) = 1. y = Preview Points possible: 1 Unlimited attempts.

Answer 1

Solution: us dy 54 +46 dt with initial condition 910) = 1 Can be wutten a as egn dy 54= 46 at Dividing by yo on both side we get 4-6.dy - 5 4-5 = 1-0 put 4.5 = v dv = - 5 y 6. dy dt on, dt 5 at using above in ean . weget sell lugt - m - 5 v = 1 or 00 dv + 25 V=-5 dt This is linear Iquation.cohose integrating factor is. e$25 at eest V. east Aca 285 V. east UT, Solution is V, 0254 :sseast + CD = -8.east - 1 east to V= - + c put v=y-s in can weget 4.5 = 3 + c ys + c.e-2st east Oy east ㅗ = 5

Now, 11 sh - + c.e-25t PIL using initial condr. y (o)= 1 Ś + C.6-2580 obiad door rold ta PP! S s[of] = (0)5 - 1 5 3 ba C = Ś + 1 CE 6 5 putting the value of c in ean & we get js = = 5 + -25+ 1 = VU- c = vastvo or y 6e-254-1 alatul 5 per place laat مر y s = / (61-25 t - 1) on y= (.6e-25t - 17-14 Nort His OT, y= ys в [Geze 6e-2st - 1 Ans.