Analisi matematica 2 - esercizi equazioni differenziali

J

x

! a*

bi] n-r

)..*

, n"*

Ite

V fir'- , x

^Jh- n,,, Jf *

r(rl - .

r) JL

4lt,

tb"l Jt

a

rr))

=11 <l{!.k

t f

I /{

I =fi[',-',"f

f(È,1[t))

b Í'u

X ìlo

o Ir{ o

x

qo*$**,"*^;b .

Uo*..*- )t,> *

De.- d.

tt

vLú k

$]{tn,qt)Utl I,,i <ìU

, "n,ì^J.f* r:r,3&)l )

f

T(r)cX

o,u-J V\uX

; 9-^o

T 5,J5.. X

r---u-^àrtu.t'--

W4-tL*,^t ,-"-ri- ,rfin*

& e$q

tt, T[t)

Ttr,) s"+ (o)

5,(LDJh

[rc) t--t bot-

=

= l)(É,,)/ú)Jó,

\-t r(q) (orîi(,,u{a)'1r)} ,

-

r,úr))dr)

U*f*

l(x.

J [i ,ln^.È-X

[u,) =

, !,v.*!

fr." X)u)L

V*u [*nt\,*"nÚ,

, IM

X. 1,",.- i

úi

r,u.iaf Jr

-

' *,(s))

- dr,

(f flf

,5,[L)),Ù*l

,,r,(tt)JL

f," L"t{

i*,f

f I

\

t\ n

dtr o

(L * nt

(o^-0'9 n")

^1&* ':!r-

, y-

@ Y. J(n,,s,) i[,nbr.fi,

,litr-,\lríi)= .

s;tt (a-r1

u u,{.È})ntbî

5ir*,

''5,tii)Jl

I ,

" ilt:."s

Pn..k _

{ug hru*

L- ,l,t

ttr- ,

,rtfr-e."-&}-*-

{À i,--}

t*À*

",^,-J ",.t**b s.* g(.*)

,

roNr(t): T{q) l, ,,,*!]

E ne

6"1= V

3 5t'ouX, fr"-

oe;J , ,."

JL) Ú

V rv-

giú) +

frr--Li

b"-

= S;?(à,

[t,,.1 j*-"*)

' ó gt^J (w

qUJf"vr--

!]

du*

c ú

-,à*'

à o-

$ff "x,-*

L''

b n"...

[u;5 '

* e-da

pLLl',*---

,i,!- ìff,

\r,* flsRt"ì*ù ,

t,ll r,^A, {,,",,à).A

, flw$*-t"".--

;

*i

I t""t--

4 ,

L-,h-a

ri A (vr^

A

vr r^. A).

L,c

u".. 3t

)5 W*

*"t fjft

Js, t' W

rJ .'-erv*'

!r., '

] ùeè- Iu"-\,y,u[*R,nf^

5tr)

{L O"-,ilrà

i ,J

*^/eu*

T*u^-* ^i*t

[rt .,"-y*^J')

i,tg$-lR

9.*

l-h, M !*

, l*Ì*-

,"f*Àr. '*It

i*,Ù r lo,L)xP

,Sù;-.-J-tR' r'

J

9*(-r,*.)e , t""k,

(u,b)xff SL ,

ullr,-r,l

-i(*,'r,11

f(*,r,) (r,,'1,

ms4"s V {,$r,

), br)o

, &ó)xp.

*..

T^

r) h^ *{r^ú*,4{

3 rq&^q

d

5t"),(u,L)'lP, r"Hà^^__

úfl

[q""" ú,J--- n

d^ i,*,{*A*,

*,*'J;0:

[Xrrru",* (.

o- -f^*È)

nsnr^o[,rr,,

9u** ;

+R

, Y[*),(u.C),oB

X("1 "

(o,b) uubn

,.fi,* W^*: *rlr,,,o^r,r*^ rti,,*

4J,fì.

['

{}u+i*,[ni*-. oryo^s -Li+

(E) - v(t)

{=X(") *i*^[.t ('

.,t /'* qdq*'"A,)

J* o*fl/.d)è.s- n6urLa.[, "

{a: *i, fi

l* f,(rc)vig)

coàe [n,d)

{o-,b)x

=

=

L^,0)

1^ofo ?

r *-. A

- Lp

J-t*^-"^^-." $-

\{oJls^ e€A** J-'

**À cq,.^sn:r,u-.

"fr^

1rdn : (",p)-R /

#r*

br d---

'l* ,

6àeAîg

?roNr

u &oRl A

SoL {q)

$")

.

"Í.,^ ,sroo i=K,rvdil,

p)

ú* x. *, Jdr--*'**

V

t* (5(":)

eok**.*- L

=o

àa- àf.^

( E"

& Y

D^" t

it ol

nl^,

d

R ro-*,h",,.-

:

(*1

t

rL rhp/td.o^e ["t,p)r

euolrSouo- ,00Ú",.-

^s- * tno

*-*ft"#

=l L(-rp)

Vre.

=o gtu)

X{*) [*rP)

V[5(,.,)) [",,e) , $C'.1:g

=

5'l*) í t*o tf-

io {t)

ulr'o

& (.r

rn! Y

9o

=à

p,:.l.J tutd ,P)

Y Ylt") ,ffit-

\ e]*

*.,

\t.- [*) YÚq.)"",

f"U

oL €Fnu,5e [.,d-)

zon I

\lj.&,b*..- O. J tL (q) î*

{* eak{

.

t*ú^ -

J,l-.-Lo- bffi,

0..-

V [o '-",-

x,o

= f-n,

$o

$b") , 1,p) *k^k

.t

*k {t) ù,* ?-

Nhr .^b?t"r-; &S

I

Li". ,rU

0. g'",t

1* "

Ba^,}

br' qb

u t \(t).(*-

d

(a,F)

:.,6o

gt") tu^,

io-,!) ?-r"

b"

e

'- \(*J" o).

.

: #r

,J,,^--

L- (*,B) tol

Jff*

Dr

$oltrZrsrur d

-rlR J,u"

a,

eA:;€,e,.oRtA $(*,),

o,

ú ry (t(')) (",F).

to. Jt

e^hg"u"- t

r* V ú

t"

R" -.*"t" *úrà. r*n,fr#l--

Y

.L' t

*ù^

\q \

uo.hyrro-

Qf)ulrJls*o $-)'Y'1* z* (r)(,.r) *o Vx*

"ftr,* ("1p)

,

,J -^-Un" Vvu(o,F),

Y[,5r,0)

${.,ù=K(0,) /_lc.9+sryL lW

*t

,*LfL*

*l^- t)"

€lt ,^t,.) .,@*^f*rrt"00^ .1*-^ù

In'..,

fi,>rri"ts 1*,F)i

^-0t'.^6,rr

?*;^. ,5;-k^&)

dt u

(r,t) i^[

(",qrt ,

1:u.5[*t'[x,()

I)r&^gù4b

l-,,*$5t*) (x,,

=

*s

\[q) a

paydcl'--xc(..,ef)

Y[ttq)=o

[x,l)-]*y*l

V5. [,,ffiL**"t'

(t,t) **

*"ù

-

s) (r,l)*lR

9(f),

9,.,-.o h,

ol

pr;Lnso

Lira,- *e

h tf

(t,t) ìlB, (o,b)

aN

X(-)

",*

, @Jvr-rfu-

F[',.,,) ,