yesterdayFayysinxtx2e7y

FFEM

M 3xytyt Xd FfgN x'try MGM N xg Fg

Ttp deck if My_Nxy g

h

1453 12 exactness

N 2xtyMy4 Nx

Thisequation is not exactlyDONEthismethod will notwork tofind thesolution

14 4 5 tKx'sµ 2 222g 7 3 4 3 7 3

check My NxMy 4x2gTHE 8xyttextNx 4g2 7.3 2 8xy 21

2

Its exactif My Nx11 21

Ourequation is

4xy 2k2g 2 22y 73y o

14 4 92 21x'yN 2 72y 7

3

we knowits exact fromabove

TEI S4 5 21 3 d treat antphi fee

FCxis 4g 21 lotsF xn 2 3,2 7x3y tolls

STEPI Fy 2x 7 370 S

set Fy N

4x2y 7 3to G 4 3 7 3

flood fo10G C

FG 9 2 292 7 3

general solution

2 242 73 C

Modelingfassumeamonthis30days

15.30 450micepermonth

dependsonpopulationdependsontheinitialpopulationIstheamountaddedbyreproduction more or lessthantheamountkilledby predation

Twoscenarios i Howmanymiceafter1month ifthestartingpopulationis

A P o 600 miceaddedbyreproduction 300Killedbyowls 450totalafter I wonthe6001300 450 450

B pfo 1000 micereproduction 500Killedbyoils 450total 1000 tSOO 450 1050

y 9 92 Goal y fsexy

y 9 4yd2xy

y 924 22

5fat 2

y EHI't2STEP1 lety xSteps Guess y ay

y

u.it a X

substitutewww.fs i the

separatevariablesu u

Wxe Itu1Zu u4 U'x Is4tu 4

Uk IttadividebyTudx dx

9 4 In Htcsitmplify uHiplytopandboltonby24

g2 u'd

ftp.tdxU b l Il l legate

Use substitution to integrate1etw 9t2udw4uduTuzdw

udufsuISZ.tdw

If IdwII Hth 19124 _In Htcsolvefor uIn191244 241 1 1 2C

elnl9t2u4 flak 1 2C

191244 e2klxlt2c

19they Kek

19ttuy ehlxY.ec

9t2u4 lx4e2cnInegafiu.x2T'isnonnegative so 1 4 12

9t2u2 eng g

2a2 x eh 9T 2

I 2

42 12 22e IzU FEE

y ax

5 IEEE X

theproblem asks for yd so lets squnboth

Y

asides

y f FEE x2

y x'e E xd

y2 Ex9ek_E