Question

please help me and show all the steps and make sure it's correct

1. (a) A calf weighs 55 pounds at birth. As she matures over the next t years, her weight grows at a rate that is directly proportional to the difference between her estimated maximum weight of 1200 pounds and her current weight of w pounds. Set up and use seperation of variables to solve the DE and find the weight function w(t) (b) du Use seperation of variables to solve cu = usin(vº) with u(0) = -1 dy

Answer 1

given weight of at between 1200 and Calt birih = 55 pounds W(o)-55 weight grous proportional difference Current weight of 'W' pounds ie dw (1200-w) aq Removing proportionality and introducing some Constant K dw KC1200-) ar Solving pst order differential equation J kat -In (1200-W) = (t +f-me] where (incis constant of integration InCl2oow)-ino) dw J 1200-W in (1200) kr. -kt 1200-W се 사 WHE 1200 ce using initial Conditions to. find cak - وانه -KCO) 55= 1200 C CE 55-1200 11451 C- ) -kr llase So Wit = 1200 Hence is weighted function kt WCHS 1200 - 1145e * T

( 5 ) du av sin (42) ucol = 4 dy - du u Y sin(42) ay bols Integrating sides se on ju sin cuy ay jus v=t- 1 usincu 2 du Incula act rudvadt V dva in (4) at sin (4) det į tcost of c -cost where Casintegration in(u)= Constant in (4) fc

(u) ال ما 나C ecc- c빨 Vit Jesubstine 인 u) | e-Coyo) 을 -1. e 면 el er Y2 e. e u = ec Cost e 42 /اكمام 빨 -Ct + cs ur e (at) uch- e Answer