Esercizi Cauchy con metodo di somiglianza e di Laplace - parte 4

S

-

:

fls) *

S 3

-

As R F y

90 1

+ + +

+ 3

c -

33s =

-

-

E A

A f Tg

B =

+ = B

-

3B Y6 c

+

- c 3B

= +

-

= -

91 1

3 =

-

9( 3 ft 3B)

% B) 1

+

- =

-

* 4

93 93

+ 1

=

- -

18B 4

1 4 B 0

-

= =

- -

1

A = 1

c

E

& = - e

As As

As ·

- t

3

to Te -Le

% t

sins

- 18

est

& y" 2y

+ = (

y(o) )

Y Y =

= ;

13

x =

9

x

6 = -

9 0

=

+ Avin(t) Bcorbt)

Yo +

= Aest

=

Yp Aest

Y S

= 9D2

"

% = st

9Ae3t

+

9Ae3 e

+ =

=

1

18A D

=

Fest

Yo : He

Cc00(t)

(3t)

y(t) +

+

G won

= est

(3t) 3(win/34) 1

y'(t) 4 co) +

3 -

= to C &

t =

C + = T

% C = "

032

% -

=

34 =

+ et

y(t) f

sin(t) +

-

=

& sin(t)

y" 3y1 by

+ =

- y(0)

y(0) 0

= =

=

* 3x 6 4

+ =

- 3

-

* 2 -2

t

3

Celt-ce

Yo =

Yp A 2t cosat

B

sin

= +

Yp 2Aco2t-2Brinat

=

y It

-Amin2t-4B co2

= lostruct

10D cost

cost

Sinst-33 +

ha -

- ukt)

63 coret

61 Winst =

+ +

4 4A 60

10B 1

+ + =

- 6B

<B 0

10A =

+

- -

E 10B &A

1

CD + 1-10B

= =

A Y

2B-10A 0 5B

=

= -

1(k 3B)

2B 0

=

-

-

2B 5 SB

+ 503 =

0

- 5 B

=

= = 52

1

A I 1

= A

- = 52

Ip A minut cost

I

= + 32

t

3

t

2 1

g(t) sinct 5 cost

+

Ge Ce +

f

= 52

3t

*

y'(t) 1 sinct

-I

3

2 Ce cos2t

Ce

+

= + 26 26

( Eq

+ Cz

C

2

+ -

= - /

0

1 I 34

24 + =

0

24 +

= -

36 +

+ -

26

E3 Git

-

=

+ C

Es

C C =F =

= Ct es 1 sinst t

y(t) 1 cost

↳ +

= t

- 3

& sin(t) l

y" 3y1 by

+ -

=

- a

6 +

L

y((0)

y(0) 0

0 = -

= s 4

+

3f(0) 6f(s)

if(e) 1(() 52f(x)

sf(0) +

+ =

- th

-

- 68(x)

if(s) 3ef(s) 1

=

+

- s 4

+

6)

A(s(s =

5

+ =

- 82 b

+

palT

1(x) = 3)

( 2)()

6) >

- -

-

+

+, 4)() 2)

c(z 3)

2)(s

(a) b(22

b)(s 3)

2)(s 2

+

+

+ + -

- =

+ - - DCTLD

c

As 4C

+

bs-2DS-2B

+ 352

CS 12C

3As 3Cs

2AS" 6B

bs"- 6As -

3 +

+ -

3B3

As +

+

2DS-

+ -

- 2DS2

DS ED 2

(D) - =

- -

+

4 A

A C D

+

c D q

+ =

= -

-

30 3C-ID

* 2A -

- 0

=

- =

4D

2B 4

33

- 64 +

+

+

- 8D

6B 2

12 =

-

- A

4 D

c

A -

+

c D =

q

+ -

= SA

B 3C 2D

+

-JA-3C-ID +

+

=

0

=

B 4D

4

60

SB C

+ + 0

=

+

- 8D

6B 2

12 =

-

- 6(c

5( b)

2) 4D

4

+ 0

+

+ =

3 +

5A +

+ -

- +WD 0

=

4C

25( 6D

6C +

D) 10D

15c -

-

c - -

-

-

- d

-1

c

8 =

13D =

+ 0 A + D

A BB = =

D

+

- E

!)B

3)

3(3D) 2 0

=

B -

-

-

- 29D 0

21

B 21

+ -

- E 1 D

B

D =

+

B = 12/ BD)

6((D) Ed 2

- -

- =

D

(D 2

-D =

ED

+ D 2

=

- 13

1

1 E

B I

.

= 26 E

.

B

* I

= 52

=

2

13 -

-

c = q +

+,

FG d

foto A +i

-I

& t

& s

92th

82 st

e

Irinkt) -1 e

5 co22t

y(t) + 5 s

= E2

Felt

E y 2g = -

- (0)

y

22 0

(0) =

=

y IK

=

p 2x =

x

0

q =

- -ret

ret

+

Cre Cl

y +

= Atert

Ip = ret

Aeret raAte

yp +

= eBeret

Vet

Veder

yip Late

+

= ret

ret

e-2Atekt

Vet

Veseret -Re

2A =

Late

E 12

- 2/2B -

VeD VD A

= =

+ = 0

2A &

=

20 0

- = Vet

te

-

Yp =