Esercizi Cauchy con metodo di somiglianza e di Laplace - parte 3

D A

0 4C

=

- =

hB 3

2D 4 A

+ 3

- = =

8C 4 4

+ + 3

= 3

B = -

16 16

c = se

is

+

is

=> I <

ac

& It

te -

t

2

& 2

e e

+

16 16

It

E -

y 2y 8y e

=

- - =

0y(80)

y(0) = 8

2x

1 0

=

-

-

-

t

Ge 4

Ce

+

Yo = It

e-

At

Yo = <Ate2t

Beft

JP -

= 2t

hAtE2-2Ae

- LD2 -

Yp" +

= it

It It

E-CAE -It

-

-

- GAte hAte-sAte 2

4De =

+ +

- -

1

4D 20 1A

60

= =

-

- =

- - 8A

hA

4D 0

+ + 0 0

= =

It

-

-Gte

Ip = It t

4 f tett

-

(b Ge

y + -

= * At t

"Elec

-ect

Y' +he +

-

y(0) 0

= C1 Cn

C -Cz

0

+ = =

4/

y'(0) = 1

44 1

2(1 + =

- -

2(z k( =

+ + 1

C1 -

= 18

1

!C

64 =

= 18

et

It It

- -

Ste

e +

y -

= - It

E -

y 2y 8y e

=

- - =

0y(80)

y(0) = 2f(d)

Crf(x)

f(()

if(s) Sf(d) +

-

-

- 1

8f(x) =

- S 2

+ I

8f(x)

21f(x)

if(s) E =

-

-

- 8 2

+

8) #

f(x))s 161p3t

25 = +

-

- +

2)(3-2)

f(x) (s st

+ = -

M 4

-4

32

+

sti + -

+

Als) = I -

2 2

-

4)

( 2)(s

+ -

A ( +, 16 +

t =

(8t2 2)

B(s t

2) 13

2)(s c(s

4)

B(c + +

+ + =

+

- -

28

BS + =

<SFHCsth 1 StL

A 8 - hA BS2- 8 B =

UBS

+ +

<BS + -

B c 0

+ B

= C

= -

16

A t

3

2B

4B + A 2B 3

+

+ = =

-

- 1

a 2

= +

(D =

8B k

+

-

- 1

A 4

2

= -

-

A 1 64

= -

4(5 6) ↳

8c x

- + + =

- 3

↳

2

24 B +

8 + =

+

- 3 i

63 36C 2 C

36c =

= -

= (8) -

=

7

1

A 6 .

= =

-

=

- Po

B = - 2t

* 4t

-

12

1 +e

te +

- If

18

62 - 37

y" qy -

4 =

- 1

,

y(0) 1y 8) =

= =

x =

34 3

=

p

9 0

=

- 3t

t

3 -

Ge

Ce +

Yo = 3 t

-

Ate

Yp = SATest

*

Be3

y'p = - qAts

- 3Aj3t

-3 D23t

y =

p _ &At t 3 t

GA23t gAtE3t be-

+ =

- - A 1

6 =

GD -

=

- 9A 9A

+ 0

=

- o 0

=

te-st

yp -

=

Cne3* cast test

y(t) +

= -

3 t 3t

It

*

3Ge -

y(t) -

- ste

3Ce +

2

= - -

y(0) 1

= 1- Cz

Ce

Cn C 1 =

+ =

'(0) 1

y = 3(

3(1 1

1

- =

- (1

3 =

3( 2

3 = 6

-

- =

C

6(z 1

= -

- st

st -

5/23t - te

+

y(t) e -

= e

ber

gi- gy 1

& = S 3

+

98(x)

f'(0) 6

of

if(s) (0)

- - =

- 5 + 3

sf(x) 9f(x) ↳

1

r

- - =

- S 3

+

9)

f(x)(c 5 +

=

- s 33 3 3

+

+ +

/3

f(x) 9) ste

- : casts

A(s) e

=

1 1 34s

1

+ + 9

+ +

=

(2 3)(2 3)/3- 3)

+

+ = S

3)

A(s 3) c(s

3)

3)(2

B(s + 4) 3

+

+ + +

- - = +

+ 3

BS 38

+ 9 65

+ +

As 3D + 12

- +

*S +SYthSt S

6C)

Cs2

9 B

3BS 92

- +

+

- =

+

4 l

B C

+ = B 1 C

= -

A 4

6

+ = A 4 62

= -

9

9B 9

31 + =

-

- 18 9

9 9

+ 9 =

-

1 +

+

- "

36C 30 c

= = 1/6

3A 1 B

4

A =

-

= - = 1

+

1st y +

+ 6

-- 6 S 3

Sas -

3)2 3 t est

st -

- 3

ye /

te +

+

- ·

6

bet

\ y" =

3y

+ = -

(0)

y

(0) >

y = 3f(x) 3

sf(x) 3 +

+ = 1

S +

Fits

-(s)/s c) =

f(s) Ella -

-

+

B E ps

-

=

bet

\ y" =

3y

+ = -

(0)

y

(0) >

y = ;

a 3

06 =

3

+ = = (21n(v3)]

[(cor (3)

2

% +

= Det

yp = C

-bet

y =

↑ t

y"p -

Se

= Net t

se -

3 32

+ = 3/

A

HA 3 =

= t

-

34

yp = t

-

(st) (rst)

y(t) Cncor e

(2

+

= nin + t

y'(t) (sin Vettrs(scorkret-E

-

= ,

y(o) = 0 3

0(

3y = -

(n =

+

y(0) 3/

= - 3( 3

+ -

- =

Cz d

= t

co(t) 3,

y(t) +

3

= - ,

23t

d y" ey =

+ Y ( )

(2

y =

= g #

p 31

96

9 =

+ 0

= = =

-

(C (t)

cor(t)

i Czern

Yo <

= t

3

Ae

Yp = 3D23t

I'p = Best

"p

y 9

=

9123 3t

t

3

9ae

+ e

= Te

91 =

2A 1

+ =

st

Fo

Up e

= t

3

(ecoskt)

(t) /3)

< sin Le

y + +

= 18 t

3

y(t) (3t) 3 Lecort)

3(vin +

+

= -

T

y(o) = T C 0

T

Ce =

+ = f

1 0(

34 + = = -

the

- Asin(st)

y(t) +

= est

(y" By =

+ Y ( )

(2

y =

= g 3f(x)

if(s) 10 + =

- =

3)

f(x)(e2 A +

+ = ↓ -

Als)-stit

e 3)(s

(s 3)

+

-

A E) Ha ste

1634 +,

- =

-3)

/BS 3B)(s 2/2 63)

3)

* + 30

s + 9 -

+

+ +

- ...

=

CS

2 33s

B)

31

As 9 -

+ 6Cs

+ 3 BS 9B

+

- +

+

-

t

=

C

BT

E 16

-62 =

* -

9

30 1

9B + =

- # c

B = - 6C

A +

= y 9

9

+ +

1 18 1

=

+ -

- t

t +

+

1

36 = 13

f A

B +

0

=

c = -

= 16

A =

+ To

Fin

Y is

I

t -

( (s 3)2

-

(ii)

5 it

sin(t) He

+

& y" vin(2x)

3y1 by

- + =

y'l-e

yloy 0

=

=

x 3 6

+ 0

= 3

di -24

=

, = -

2

3 It le Xe

soluzion ,

Yo G2 Cze

+

= perche

coincidono

non reali e

Barkt)]

(Arinht sin/cos i

>

-

+

Yp = Cos- -sin

>

2AcoCE-CBsinat

Yp sin

=+ - cas

-p sin2t-4BCorst

-40

= Beinst

Doset

Asin2t-4Bcoret-10 +lo

- >

- - nin(t)

GBcosst

It =

6Asin

↓ +

4 4D 61 LoB

10B

+ 1 1

2A

+

- -

=

= H 12 3B

= -

↳B-10D GB 0

+

- = 1

A

4 B 6 B

JOB +

5 0

+ =

- - = S2

=

B

52 B 5

= 52

cosht

&

It

1

Yb sin +

= 82

32 an + cost e

3)

yvineE

(t) Ge

Ce + +

y = 3t Cret

y'(t) cost sit

3212 2

+

= +

4 C 1 - C

-

=

4 E o

C

+ =

+ Sz

- = e

222

3 =

+ + top

C =

-

24 =

e 3 + +

- - + 1

C

i

C -

=

= -

- S2

-

C2 =

123t

y(t) - coset

inst

= - t 82