Possible ProblemsTopicsI Separationofvariables2Methodof integrating favor3Stability equilibriumsolutionssolution curves autonomous DES

4slopelawnon fields

5Euler's Method La steps global error 0 h

6 Modeling Population Compounding interest Newton'S Lawof Cooling wongModelmixtures

t Orderof DE meannonlinear homogeneousInonhomogeneous8Solutionsof higherorder DES with operationapproach or characteristic equation9 wear dep.lmdep.Wronsk.is fundamentalsetof solutions10 ⺕ of solutions

Ex Show that I andxlxlareUI.citczxlxkoltx.S.nu

it has to be true for all x it's true atsayㄨ1⼀如1 a t a 0 M x ㄨ20

⼗ ⼆ za o c.noㄨ 1 a a 0 Ma 0i 5 and

xlxlarelI.SIBFndaDE whose general solution is yiiětt Getroots 2 3

RD D 2 D 3

DE B RD y 0D 2 ⼼ yo5 126 yo y t y 6y 0

Euler's Method䘡 fcx y ycx y

N of steps h ⼆ 州哥

xntFNnthlyntii.yntwfynynq.iranimation

Weknow error 1yexatlxf yN l c h

if h ⾥ error is terror

Ex 䘡 ytttētus too 㼦 y 七 equilibrium solutionyttt.noyet

Ifasy yz tasympun.cag

巫 Write DEfor wnimyctklast 0

mgat 1 y y 1 equilibrium solution

y n El7__巫 y y 1 2 y i

as too 㼦 ytt 器 y t

m d吣北⼆efdtetuy.int 㗊 㤈

莲 草器eiyft.tdttcyt.lt cě

亚 Solve y 5y o

5 5 yDCD57y.noD 0 Dz 5

y C⽐ the at a⽐

赵 瓷⼆5以3⼼ 7⼋乃⼼⻔

qui solutions ㄨ 3 Eh to 必 1

xaiAAvifn.ITsemistone x Efㄨ 0 unstable 3

2Kl stable7t.rounstable

7X