Ecuaciones Diferenciales - cb.mty.itesm.mxcb.mty.itesm.mx/ma2001/alumno/tareas/ma2001-hw-7b.pdf ·...

Ecuaciones DiferencialesTarea No 7: Transformada de Laplace

Maestra Ruth Rodrıguez, Agosto-Diciembre 2018

Grupo: Matrıcula: Nombre: Tipo:-1

1. Cual de las siguientes opciones representa la transformada

de Laplace de la funcion:

f(t) = 5 + e2 t + 4 t

A F (s) = 8+14 s+6 s2

s2 (2+s)

B F (s) = 20s3 (2+s)

C F (s) = 20(−2+s) s3

D F (s) = −8−6 s+6 s2

(−2+s) s2

2. Cual de las siguientes opciones representa la transforma-

da de Laplace de la funcion: (Sugerencia:Use identidades

trigonometricas para eliminar el cuadrado)

f(t) = 2 sen2(8 t)

A F (s) = 2(

1s − s

256+s2

)B F (s) = 1

s − s256+s2

C F (s) = 2(

1s − s

64+s2

)D F (s) = 1

s + s64+s2

E F (s) = 14 ( 1

s − s256+s2 )


de Laplace Inversa de la funcion:

F (s) =2 + 4 s + 8 s2

s5

A 4 t2 + 43 t

3 + 12 t

4

B 83 t

3 + t4 + 25 t

5

C 8 t3 + 4 t4 + 2 t5

D 4 t2 + 23 t

3 + 112 t

4

E 43 t

3 + 16 t

4 + 160 t

5

F 8 t2 + 4 t3 + 2 t4


Inversa de Laplace de la funcion:

F (s) =2 + s

(−10 + s) (−5 + s)

A 65 e

5 t + 115 e10 t

B − 125 e−10 t + 7

5 e−5 t

C 115 e−10 t − 6

5 e−5 t

D 65 e

5 t − 115 e10 t

E 125 e−10 t − 7

5 e−5 t

F − 75 e

5 t + 125 e10 t

5. Indique cual de las siguientes opciones representa la trans-

formada inversa de la funcion:

F (s) =−4

12 − 8 s + s2

A f(t) = −1 e−6 t + e−2 t

B f(t) = e2 t − e6 t

C f(t) = e−6 t + e−2 t

D f(t) = e2 t + e6 t



F (s) =−45

(4 + s2) (49 + s2)

A f(t) = cos(2 t) + cos(7 t)

B f(t) = 12 sen(2 t) + 1

7 sen(7 t)

C f(t) = 12 cos(2 t) + 1

7 cos(7 t)

D f(t) = − 12 sen(2 t) + 1

7 sen(7 t)

7. Utilizando Transformada de Laplace, resuelva el problema

con condiciones iniciales y(0) = 0 y y′(0) = 0 y ecuacion

diferencial:

16 y + y′′ = sen(6 t)

A y(t) = 340 sen(4 t) − 1

20 sen(6 t)

B y(t) = 310 sen(4 t) − 1

20 sen(6 t)

C y(t) = 120 s sen(4 t) − 3

40 sen(6 t)

D y(t) = − 340 sen(4 t) + 1

20 sen(6 t)

Ecuaciones Diferenciales, Tarea No 7: Transformada de Laplace, Tipo: -1 2

8. Indique cual de las opciones siguientes es la ecuacion sub-

sidiaria del problema con condiciones iniciales y(0) = 2 y

y′(0) = 0 con ecuacion:

49 y + y′′ = 2 cos(7 t)

A Y (s) =s (100−2 s2)(49+s2)2

B Y (s) =s (98+2 s2)(49+s2)2

C Y (s) = 100+2 s2

(49+s2)2

D Y (s) =s (100+2 s2)(49+s2)2



Grupo: Matrıcula: Nombre: Tipo:0



f(t) = −5 + e2 t − t

A F (s) = −2−11 s−4 s2

s2 (2+s)

B F (s) = 2+9 s−4 s2

(−2+s) s2

C F (s) = 5s3 (2+s)

D F (s) = 5(−2+s) s3



trigonometricas para convertir un producto en una suma)

f(t) = sen(2 t) sen(5 t)

A F (s) = 12 s

(1

9+s2 − 149+s2

)B F (s) = s2

(4+s2) (25+s2)

C F (s) = s(

14+s2 + 1

25+s2

)D F (s) = s

(1

9+s2 − 149+s2

)3. Cual de las siguientes opciones representa la transformada


F (s) =7 − 4 s

9 + s2

A −4 cos(3 t) + 73 sen(3 t)

B −4 cos(3 t) + 7 sen(3 t)

C −4 cos(3 t) − 73 sen(3 t)

D 7 cos(3 t) − 4 sen(3 t)

E cos(3 t) + sen(3 t)

F 73 cos(3 t) − 4 sen(3 t)



F (s) =7 + s

(−9 + s) (−2 + s)

A − 97 e

2 t + 167 e9 t

B − 167 e−9 t + 9

7 e−2 t

C 167 e−9 t − 9

7 e−2 t

D 37 e

2 t + 107 e9 t

E 107 e−9 t − 3

7 e−2 t

F 37 e

2 t − 107 e9 t



F (s) =9 + 9 s

−48 − 2 s + s2

A f(t) = 8114 e−8 t − 45

14 e−6 t

B f(t) = 8114 e−8 t + 45

14 e−6 t

C f(t) = 4514 e

6 t + 8114 e

8 t

D f(t) = 4514 e−6 t + 81

14 e8 t



F (s) =−77

(4 + s2) (81 + s2)

A f(t) = cos(2 t) + cos(9 t)

B f(t) = 12 sen(2 t) + 1

9 sen(9 t)

C f(t) = 12 cos(2 t) + 1

9 cos(9 t)

D f(t) = − 12 sen(2 t) + 1

9 sen(9 t)



diferencial:

4 y + y′′ = sen(5 t)

A y(t) = 121 s sen(2 t) − 5

42 sen(5 t)

B y(t) = 521 sen(2 t) − 1

21 sen(5 t)

C y(t) = 542 sen(2 t) − 1

21 sen(5 t)

D y(t) = − 542 sen(2 t) + 1

21 sen(5 t)




16 y + y′′ = 7 sen(4 t)

Ecuaciones Diferenciales, Tarea No 7: Transformada de Laplace, Tipo: 0 2

A Y (s) = 28+112 s+7 s3

(16+s2)2

B Y (s) = 28+28 s+7 s2

(−16+s2)2

C Y (s) = 28+28 s+7 s3

(16+s2)2

D Y (s) = 28+112 s+7 s3

(−16+s2)2






f(t) = −3 + e−3 t + 3 t

A F (s) = −9s3 (3+s)

B F (s) = −9(−3+s) s3

C F (s) = −9+12 s−2 s2

(−3+s) s2

D F (s) = 9−6 s−2 s2

s2 (3+s)


de Laplace de la funcion: (Sugerencia: use las definicio-

nes de las funciones de las funciones hiperbolicas mediante

exponenciales)

f(t) = −5 cosh(t) senh(t)

A F (s) = −5 s(−1+s)2 (1+s)2

B F (s) = 5(2−s) (2+s)

C F (s) =−5 (2−s2)

(2−2 s+s2) (2+2 s+s2)

D F (s) = 5 s(−1+s) (1+s) (1+s2)

E F (s) = − 15

1(2−s) (2+s)



F (s) =8 + 6 s

4 + s2

A 4 cos(2 t) + 6 sen(2 t)

B 6 cos(2 t) − 4 sen(2 t)

C cos(2 t) + sen(2 t)

D 8 cos(2 t) + 6 sen(2 t)

E 6 cos(2 t) + 8 sen(2 t)

F 6 cos(2 t) + 4 sen(2 t)



F (s) =6 + s

(−9 + s) (−2 + s)

A − 157 e−9 t + 8

7 e−2 t

B 107 e−9 t − 3

7 e−2 t

C − 87 e

2 t + 157 e9 t

D 37 e

2 t − 107 e9 t

E 157 e−9 t − 8

7 e−2 t

F 37 e

2 t + 107 e9 t



F (s) =−1 + 5 s

−s + s3

A f(t) = 1 + 3 e−t − 2 et

B f(t) = 1 − 2 e−t + 3 et

C f(t) = 1 − 3 e−t + 2 et

D f(t) = 1 + 2 e−t − 3 et



F (s) =45

(36 + s2) (81 + s2)

A f(t) = cos(6 t) + cos(9 t)

B f(t) = 16 cos(6 t) + 1

9 cos(9 t)

C f(t) = 16 sen(6 t) + 1

9 sen(9 t)

D f(t) = 16 sen(6 t) − 1

9 sen(9 t)



diferencial:

9 y + y′′ = sen(4 t)

A y(t) = − 421 sen(3 t) + 1

7 sen(4 t)

B y(t) = 17 s sen(3 t) − 4

21 sen(4 t)

C y(t) = 421 sen(3 t) − 1

7 sen(4 t)

D y(t) = 47 sen(3 t) − 1

7 sen(4 t)





64 y + y′′ = 2 cos(8 t)

A Y (s) = 130+2 s2

(64+s2)2

B Y (s) =s (128+2 s2)(64+s2)2

C Y (s) =s (130+2 s2)(64+s2)2

D Y (s) =s (130−2 s2)(64+s2)2






f(t) = cos(5 t) + 2 sen(5 t)

A F (s) = 10+s25+s2

B F (s) = 5−2 s25+s2

C F (s) = 10−s25+s2

D F (s) = 5+2 s25+s2




exponenciales)

f(t) = −2 cosh(4 t) senh(4 t)

A F (s) = 8 s(−4+s) (4+s) (16+s2)

B F (s) = 8(8−s) (8+s)

C F (s) = −8 s(−4+s)2 (4+s)2

D F (s) = −2(8−s) (8+s)

E F (s) =−2 (128−4 s2)

(32−8 s+s2) (32+8 s+s2)



F (s) =7 + 2 s

25 + s2

A 2 cos(5 t) − 75 sen(5 t)

B 7 cos(5 t) + 2 sen(5 t)

C 75 cos(5 t) + 2 sen(5 t)

D 2 cos(5 t) + 7 sen(5 t)

E cos(5 t) + sen(5 t)

F 2 cos(5 t) + 75 sen(5 t)



F (s) =4 + s

(−10 + s) (−5 + s)

A 65 e

5 t − 115 e10 t

B 145 e−10 t − 9

5 e−5 t

C 65 e

5 t + 115 e10 t

D 115 e−10 t − 6

5 e−5 t

E − 95 e

5 t + 145 e10 t

F − 145 e−10 t + 9

5 e−5 t



F (s) =7 + 3 s

−27 + 6 s + s2

A f(t) = 53 e−9 t + 4

3 e3 t

B f(t) = 53 e−9 t + 4

3 e−3 t

C f(t) = 43 e

3 t + 53 e

9 t

D f(t) = − 53 e−9 t + 4

3 e−3 t



F (s) =45

(4 + s2) (49 + s2)

A f(t) = 12 sen(2 t) + 1

7 sen(7 t)

B f(t) = 12 cos(2 t) + 1

7 cos(7 t)

C f(t) = 12 sen(2 t) − 1

7 sen(7 t)

D f(t) = cos(2 t) + cos(7 t)



diferencial:

36 y + y′′ = sen(3 t)

A y(t) = 127 sen(3 t) − 1

54 sen(6 t)

B y(t) = 154 sen(3 t) − 1

27 s sen(6 t)

C y(t) = 127 sen(3 t) − 1

9 sen(6 t)

D y(t) = − 127 sen(3 t) + 1

54 sen(6 t)





49 y + y′′ = 7 sen(7 t)

A Y (s) = 49+49 s+7 s3

(49+s2)2

B Y (s) = 49+343 s+7 s3

(49+s2)2

C Y (s) = 49+49 s+7 s2

(−49+s2)2

D Y (s) = 49+343 s+7 s3

(−49+s2)2






f(t) = e−4 t + sen(4 t)

A F (s) = 4 s+s2

(−4+s) (16+s2)

B F (s) = 4(−4+s) (16+s2)

C F (s) = −4(−4−s) (16+s2)

D F (s) = −32−4 s−s2(−4−s) (16+s2)




f(t) = cos(5 t) sen(3 t)

A F (s) = 24+s2 + 8

64+s2

B F (s) = 12 ( −24+s2 + 8

64+s2 )

C F (s) = 5 s(9+s2) (25+s2)

D F (s) = −24+s2 + 8

64+s2



F (s) =2 − 6 s

36 + s2

A −6 cos(6 t) + 13 sen(6 t)

B cos(6 t) + sen(6 t)

C 2 cos(6 t) − 6 sen(6 t)

D −6 cos(6 t) + 2 sen(6 t)

E −6 cos(6 t) − 13 sen(6 t)

F 13 cos(6 t) − 6 sen(6 t)



F (s) =8 + s

(−7 + s) (−2 + s)

A 3 e−7 t − 2 e−2 t

B 85 e−7 t − 3

5 e−2 t

C −3 e−7 t + 2 e−2 t

D 35 e

2 t − 85 e

7 t

E 35 e

2 t + 85 e

7 t

F −2 e2 t + 3 e7 t



F (s) =−1 + 7 s

−s + s3

A f(t) = 1 − 4 e−t + 3 et

B f(t) = 1 − 3 e−t + 4 et

C f(t) = 1 + 3 e−t − 4 et

D f(t) = 1 + 4 e−t − 3 et



F (s) =45 s

(36 + s2) (81 + s2)

A f(t) = sen(6 t) − sen(9 t)

B f(t) = cos(6 t) + cos(9 t)

C f(t) = sen(6 t) + sen(9 t)

D f(t) = cos(6 t) − cos(9 t)



diferencial:

9 y + y′′ = sen(5 t)

A y(t) = 116 s sen(3 t) − 5

48 sen(5 t)

B y(t) = 516 sen(3 t) − 1

16 sen(5 t)

C y(t) = 548 sen(3 t) − 1

16 sen(5 t)

D y(t) = − 548 sen(3 t) + 1

16 sen(5 t)




16 y + y′′ = 4 cos(4 t)


A Y (s) =s (68+4 s2)(16+s2)2

B Y (s) =s (64+4 s2)(16+s2)2

C Y (s) = 68+4 s2

(16+s2)2

D Y (s) =s (68−4 s2)(16+s2)2






f(t) = − cos(t) − 2 sen(t)

A F (s) = −2+s1+s2

B F (s) = −1−2 s1+s2

C F (s) = −2−s1+s2

D F (s) = −1+2 s1+s2




f(t) = 8 sen2(7 t)

A F (s) = 8(

1s − s

196+s2

)B F (s) = 4

(1s − s

196+s2

)C F (s) = 4

(1s + s

49+s2

)D F (s) = 1

16 ( 1s − s

196+s2 )

E F (s) = 8(

1s − s

49+s2



F (s) =3 + 5 s + 2 s2

s6

A 2 t3 + 5 t4 + 3 t5

B 12 t

4 + t5 + 12 t

6

C 112 t

4 + 124 t

5 + 1240 t

6

D 23 t

3 + 54 t

4 + 35 t

5

E 2 t4 + 5 t5 + 3 t6

F 13 t

3 + 524 t

4 + 140 t

5



F (s) =8 + s

(−10 + s) (−2 + s)

A 118 e−10 t − 3

8 e−2 t

B 94 e−10 t − 5

4 e−2 t

C − 54 e

2 t + 94 e

10 t

D 38 e

2 t + 118 e10 t

E − 94 e−10 t + 5

4 e−2 t

F 38 e

2 t − 118 e10 t



F (s) =−8 + 12 s

−4 s + s3

A f(t) = 2 − 4 e−2 t + 2 e2 t

B f(t) = 2 − 2 e−2 t + 4 e2 t

C f(t) = 2 + 2 e−2 t − 4 e2 t

D f(t) = 2 + 4 e−2 t − 2 e2 t



F (s) =21

(4 + s2) (25 + s2)

A f(t) = 12 cos(2 t) + 1

5 cos(5 t)

B f(t) = 12 sen(2 t) − 1

5 sen(5 t)

C f(t) = cos(2 t) + cos(5 t)

D f(t) = 12 sen(2 t) + 1

5 sen(5 t)



diferencial:

36 y + y′′ = sen(7 t)

A y(t) = 778 sen(6 t) − 1

13 sen(7 t)

B y(t) = − 778 sen(6 t) + 1

13 sen(7 t)

C y(t) = 113 s sen(6 t) − 7

78 sen(7 t)

D y(t) = 713 sen(6 t) − 1

13 sen(7 t)





20 y − 9 y′ + y′′ = 4 e5 t

A Y (s) = −16+4 s(−5+s) (20−9 s+s2)

B Y (s) = 16+4 s(−5+s) (20−9 s+s2)

C Y (s) = 16+4 s20−9 s+s2

D Y (s) = −16+4 s(−5+s) (20+9 s+s2)






f(t) = e−5 t + 5 e4 t

A F (s) = 29−4 s(−5+s) (4+s)

B F (s) = 29+4 s(−5−s) (−4+s)

C F (s) = −21−6 s(−5−s) (−4+s)

D F (s) = −21+6 s(−5+s) (4+s)




f(t) = 8 sen2(6 t)

A F (s) = 4(

1s + s

36+s2

)B F (s) = 4

(1s − s

144+s2

)C F (s) = 8

(1s − s

36+s2

)D F (s) = 1

16 ( 1s − s

144+s2 )

E F (s) = 8(

1s − s

144+s2



F (s) =2 − 7 s

36 + s2

A −7 cos(6 t) + 2 sen(6 t)

B cos(6 t) + sen(6 t)

C −7 cos(6 t) + 13 sen(6 t)

D −7 cos(6 t) − 13 sen(6 t)

E 13 cos(6 t) − 7 sen(6 t)

F 2 cos(6 t) − 7 sen(6 t)



F (s) =4 + s

(−8 + s) (−5 + s)

A 3 e−8 t − 2 e−5 t

B −4 e−8 t + 3 e−5 t

C 2 e5 t − 3 e8 t

D 2 e5 t + 3 e8 t

E 4 e−8 t − 3 e−5 t

F −3 e5 t + 4 e8 t



F (s) =8 + 9 s

−8 − 2 s + s2

A f(t) = 53 e−2 t + 22

3 e4 t

B f(t) = 223 e−4 t + 5

3 e−2 t

C f(t) = 223 e−4 t − 5

3 e−2 t

D f(t) = 53 e

2 t + 223 e4 t



F (s) =−21

(4 + s2) (25 + s2)

A f(t) = 12 sen(2 t) + 1

5 sen(5 t)

B f(t) = cos(2 t) + cos(5 t)

C f(t) = 12 cos(2 t) + 1

5 cos(5 t)

D f(t) = − 12 sen(2 t) + 1

5 sen(5 t)



diferencial:

49 y + y′′ = sen(4 t)

A y(t) = 133 sen(4 t) − 4

33 sen(7 t)

B y(t) = 4231 sen(4 t) − 1

33 s sen(7 t)

C y(t) = 133 sen(4 t) − 4

231 sen(7 t)

D y(t) = − 133 sen(4 t) + 4

231 sen(7 t)





15 y − 8 y′ + y′′ = 5 e3 t

A Y (s) = −10+5 s(−3+s) (15−8 s+s2)

B Y (s) = −10+5 s(−3+s) (15+8 s+s2)

C Y (s) = 10+5 s15−8 s+s2

D Y (s) = 10+5 s(−3+s) (15−8 s+s2)






f(t) = −4 + e5 t − 5 t

A F (s) = 20(−5+s) s3

B F (s) = −25−25 s−3 s2

s2 (5+s)

C F (s) = 20s3 (5+s)

D F (s) = 25+15 s−3 s2

(−5+s) s2




f(t) = cos(6 t) cos(7 t)

A F (s) = 12 s

(1

1+s2 + 1169+s2

)B F (s) = s2

(36+s2) (49+s2)

C F (s) = s(

136+s2 + 1

49+s2

)D F (s) = s

(1

1+s2 + 1169+s2



F (s) =1 + 5 s + 2 s2

s6

A 112 t

4 + 124 t

5 + 1720 t

6

B 2 t3 + 5 t4 + t5

C 2 t4 + 5 t5 + t6

D 12 t

4 + t5 + 16 t

6

E 23 t

3 + 54 t

4 + 15 t

5

F 13 t

3 + 524 t

4 + 1120 t

5



F (s) =8 + s

(−6 + s) (−1 + s)

A 25 e

t + 75 e

6 t

B 25 e

t − 75 e

6 t

C 75 e−6 t − 2

5 e−t

D − 95 e

t + 145 e6 t

E − 145 e−6 t + 9

5 e−t

F 145 e−6 t − 9

5 e−t



F (s) =−64 + 8 s

−16 s + s3

A f(t) = 4 − e−4 t − 3 e4 t

B f(t) = 4 + e−4 t + 3 e4 t

C f(t) = 4 − 3 e−4 t − e4 t

D f(t) = 4 + 3 e−4 t + e4 t



F (s) =32 s

(49 + s2) (81 + s2)

A f(t) = sen(7 t) − sen(9 t)

B f(t) = cos(7 t) − cos(9 t)

C f(t) = sen(7 t) + sen(9 t)

D f(t) = cos(7 t) + cos(9 t)



diferencial:

4 y + y′′ = sen(8 t)

A y(t) = 160 s sen(2 t) − 1

15 sen(8 t)

B y(t) = 215 sen(2 t) − 1

60 sen(8 t)

C y(t) = − 115 sen(2 t) + 1

60 sen(8 t)

D y(t) = 115 sen(2 t) − 1

60 sen(8 t)




36 y + y′′ = 3 cos(6 t)


A Y (s) =s (108+3 s2)(36+s2)2

B Y (s) =s (111+3 s2)(36+s2)2

C Y (s) =s (111−3 s2)(36+s2)2

D Y (s) = 111+3 s2

(36+s2)2






f(t) = 5 cos(4 t) + 2 sen(4 t)

A F (s) = 8−5 s16+s2

B F (s) = 20+2 s16+s2

C F (s) = 8+5 s16+s2

D F (s) = 20−2 s16+s2





A F (s) = s(

19+s2 + 1

64+s2

)B F (s) = s2

(9+s2) (64+s2)

C F (s) = 12 s

(1

25+s2 + 1121+s2

)D F (s) = s

(1

25+s2 + 1121+s2



F (s) =3 + 5 s + 4 s2

s6

A t4 + t5 + 12 t

6

B 23 t

3 + 524 t

4 + 140 t

5

C 4 t4 + 5 t5 + 3 t6

D 43 t

3 + 54 t

4 + 35 t

5

E 16 t

4 + 124 t

5 + 1240 t

6

F 4 t3 + 5 t4 + 3 t5



F (s) =3 + s

(−6 + s) (−1 + s)

A 25 e

t + 75 e

6 t

B 25 e

t − 75 e

6 t

C − 45 e

t + 95 e

6 t

D − 95 e−6 t + 4

5 e−t

E 75 e−6 t − 2

5 e−t

F 95 e−6 t − 4

5 e−t



F (s) =−27 + 3 s

−9 s + s3

A f(t) = 3 − 2 e−3 t − e3 t

B f(t) = 3 + 2 e−3 t + e3 t

C f(t) = 3 − e−3 t − 2 e3 t

D f(t) = 3 + e−3 t + 2 e3 t



F (s) =−77 s

(4 + s2) (81 + s2)

A f(t) = cos(2 t) + cos(9 t)

B f(t) = − cos(2 t) + cos(9 t)

C f(t) = −sen(2 t) + sen(9 t)

D f(t) = sen(2 t) + sen(9 t)



diferencial:

4 y + y′′ = sen(7 t)

A y(t) = 145 s sen(2 t) − 7

90 sen(7 t)

B y(t) = 745 sen(2 t) − 1

45 sen(7 t)

C y(t) = − 790 sen(2 t) + 1

45 sen(7 t)

D y(t) = 790 sen(2 t) − 1

45 sen(7 t)




10 y − 7 y′ + y′′ = 5 e2 t


A Y (s) = −5+5 s(−2+s) (10+7 s+s2)

B Y (s) = 5+5 s10−7 s+s2

C Y (s) = −5+5 s(−2+s) (10−7 s+s2)

D Y (s) = 5+5 s(−2+s) (10−7 s+s2)






f(t) = e−2 t − sen(5 t)

A F (s) = −5(−2+s) (25+s2)

B F (s) = −15+5 s−s2(−2−s) (25+s2)

C F (s) = 5(−2−s) (25+s2)

D F (s) = 35−5 s+s2

(−2+s) (25+s2)




exponenciales)

f(t) = 3 cosh(2 t) senh(2 t)

A F (s) = −6 s(−2+s) (2+s) (4+s2)

B F (s) = −6(4−s) (4+s)

C F (s) =3 (16−2 s2)

(8−4 s+s2) (8+4 s+s2)

D F (s) = 6 s(−2+s)2 (2+s)2

E F (s) = 23

1(4−s) (4+s)



F (s) =5 + 6 s + 8 s2

s7

A 8 t4 + 6 t5 + 5 t6

B 115 t

5 + 1120 t

6 + 11008 t

7

C 13 t

4 + 120 t

5 + 1144 t

6

D 8 t5 + 6 t6 + 5 t7

E 85 t

5 + t6 + 57 t

7

F 2 t4 + 65 t

5 + 56 t

6



F (s) =8 + s

(−7 + s) (−3 + s)

A 154 e−7 t − 11

4 e−3 t

B − 154 e−7 t + 11

4 e−3 t

C e3 t − 2 e7 t

D e3 t + 2 e7 t

E − 114 e3 t + 15

4 e7 t

F 2 e−7 t − e−3 t



F (s) =−64 − 24 s

−16 s + s3

A f(t) = 4 + 5 e−4 t − e4 t

B f(t) = 4 − e−4 t + 5 e4 t

C f(t) = 4 − 5 e−4 t + e4 t

D f(t) = 4 + e−4 t − 5 e4 t



F (s) =−32

(49 + s2) (81 + s2)

A f(t) = − 17 sen(7 t) + 1

9 sen(9 t)

B f(t) = 17 cos(7 t) + 1

9 cos(9 t)

C f(t) = cos(7 t) + cos(9 t)

D f(t) = 17 sen(7 t) + 1

9 sen(9 t)



diferencial:

4 y + y′′ = sen(6 t)

A y(t) = 316 sen(2 t) − 1

32 sen(6 t)

B y(t) = 332 sen(2 t) − 1

32 sen(6 t)

C y(t) = 132 s sen(2 t) − 3

32 sen(6 t)

D y(t) = − 332 sen(2 t) + 1

32 sen(6 t)





16 y + y′′ = 7 sen(4 t)

A Y (s) = 28+112 s+7 s3

(16+s2)2

B Y (s) = 28+112 s+7 s3

(−16+s2)2

C Y (s) = 28+28 s+7 s2

(−16+s2)2

D Y (s) = 28+28 s+7 s3

(16+s2)2






f(t) = 5 e−3 t + e2 t

A F (s) = 7+6 s(−3+s) (2+s)

B F (s) = 7−6 s(2−s) (3+s)

C F (s) = −13−4 s(−3+s) (2+s)

D F (s) = −13+4 s(2−s) (3+s)





A F (s) = s(

125+s2 + 1

81+s2

)B F (s) = s2

(4+s2) (49+s2)

C F (s) = s(

14+s2 + 1

49+s2

)D F (s) = 1

2 s(

125+s2 + 1

81+s2



F (s) =4 − 2 s

36 + s2

A −2 cos(6 t) − 23 sen(6 t)

B −2 cos(6 t) + 23 sen(6 t)

C cos(6 t) + sen(6 t)

D −2 cos(6 t) + 4 sen(6 t)

E 23 cos(6 t) − 2 sen(6 t)

F 4 cos(6 t) − 2 sen(6 t)



F (s) =5 + s

(−7 + s) (−1 + s)

A 13 e

t − 43 e

7 t

B 2 e−7 t − e−t

C −2 e−7 t + e−t

D 43 e−7 t − 1

3 e−t

E −et + 2 e7 t

F 13 e

t + 43 e

7 t



F (s) =3 + 9 s

−12 + 4 s + s2

A f(t) = − 518 e−6 t + 21

8 e−2 t

B f(t) = 518 e−6 t + 21

8 e2 t

C f(t) = 218 e2 t + 51

8 e6 t

D f(t) = 518 e−6 t + 21

8 e−2 t



F (s) =5 s

(4 + s2) (9 + s2)

A f(t) = cos(2 t) + cos(3 t)

B f(t) = sen(2 t) + sen(3 t)

C f(t) = cos(2 t) − cos(3 t)

D f(t) = sen(2 t) − sen(3 t)



diferencial:

9 y + y′′ = sen(5 t)

A y(t) = − 548 sen(3 t) + 1

16 sen(5 t)

B y(t) = 116 s sen(3 t) − 5

48 sen(5 t)

C y(t) = 548 sen(3 t) − 1

16 sen(5 t)

D y(t) = 516 sen(3 t) − 1

16 sen(5 t)




25 y + y′′ = 25 t


A Y (s) = 25+5 s2+7 s3

s2 (25+s2)

B Y (s) = 35+5 s2+7 s3

s2 (25+s2)

C Y (s) = 25−5 s2+7 s3

s2 (25+s2)

D Y (s) = 25+5 s2+7 s3

25+s2

Ecuaciones Diferenciales - cb.mty.itesm.mxcb.mty.itesm.mx/ma2001/alumno/tareas/ma2001-hw-7b.pdf ·...

Documents

Transcript of Ecuaciones Diferenciales - cb.mty.itesm.mxcb.mty.itesm.mx/ma2001/alumno/tareas/ma2001-hw-7b.pdf ·...