методичка черногор

7.8

7.9

7.10

7.11

8.1

= (σ02 −

2 )e2λt ;

eλt ;

σ2A (t )= σ02e2λt .

a)

A(t )

=

A2 (t )

A0

A0

ch−1ξ;

= (σ02 −

2 )ch−2ξ;

σ2A (t )= σ02ch−2ξ.

б)

A(t )

=

A2 (t )

A0

A0

ch−2ξ;

= (σ02 −

2 )ch−4ξ;

σ2A (t )= σ02ch−4ξ.

в)

A(t )

=

A2 (t )

A0

A0

e−ξ2 ;

= (σ02 −

2 )e−2ξ2 ;σ2A (t )= σ02e−2ξ2 .

σ2A (t )= σ02ch−4ξ.

г)

A(t )

=

A2 (t )

A0

A0

8.2

t

−t

t

′

′

′

−t

a) x (t )= e

∫e

x (t )=1−e

;

(1+ξ(t

))dt ;

0

t

t

′

−t′

′

t

t

−t′

′

б)

x (t )= e

∫ξ(t

)e

′

)e

dt

= 0;

dt ; x (t )= e

∫ξ(t

0

0

2t

t

′

))e

−2t′

′

1

(e

2t

−1);

в)

x (t )= e

x (t )=

∫(1+ξ(t

dt ;

2

0

−t

t

t′

(1

′

′

−t

г)

x (t )= e

∫e

x (t )=1−e

.

+ξ(t

))dt ;

0

t

′

′

1

2

a) x (t )

= e

βt

∫ξ

)e

−βt′

β = e

−2σx

;

(t

dt ;

0

б) x (t )

t

′

)e

′

= e

βt

∫ξ

−βt′

2

;

(t

dt ;

β = 3σx

0

t

′

′

2

;

в) x (t )= αt + ∫ξ(t

)dt ;

α =1+σx

0

г)

(

)

t

(

)

−σ2x 2

∫

′

′

x t = αt + ξ

t

dt

;

α = e

;

0

8.4

dx

t

)

(t );

= cos x

+e

∫

′

′

′

a)

+ ξ

−t sin x

t′sin x

dt

0

dx

t

(t );

= sin x

+e

∫

′

′

′

б)

+ ξ

−t cos x

t

′cos x

dt

0

dx

2t

t

2t′

2

3

−3

x

x

∫

′

)− ξ(t

′

′

+ ξ(t );

в)

= x +e

dt

ξ(t

) e

dt

0

dx

1

−4

г)

=1+

(1−e

xt

)+ ξ(t );

dt

4x

9.1

= 1

= ln 3 .

a), б), в) d

H

гd

2

H

ln 5

9.4

a) dh=1; dT=1; б) dh = ln 7

;

dT =1;

в) dh = ln 5

ln 3

г) dh = ln 4

;

dT =1;

;

dT =1.

ln 3

ln 3

9.5

dh

= ln 26 ;

dT = 2;

ln 3

9.6

ln (3m −1)

dh =

;

dT = m −1;

ln k

9.7

в) x1 = 0, x2 = 1

a)

x = 0, x = −1; б) x = 0,

;

1

2

1

2

3

г)

x

= 0, x

=

.

1

2

4

9.8

0 ≤ λ < ∞

9.9

α

a) T∞

=

;

v0 = 2 χ(α−2βT0 );

β

б) T∞

=

β

;

v0 = 2 χ(2αT0 −β);

α

в) T∞

=

β

;

v0 = 2 χ(3αT02 −β);

α

г)T∞ =

β

;

v0 = 2 2χT0 (2αT02 −β).

α