1

INDICE..1

VERIFICACIN DE SOLUCIN2

ECUACIONES DE VARIABLES SEPARABLES..3

ECUACIONES HOMOGNEAS10

ECUACIONES EXACTAS..20

FACTOR INTEGRANTE.25

ECUACIONES LINEALES.29

ECUACIN DE BERNOULLI36

2

Verificar en los ejercicios que se dan a continuacin que las funciones dadas son soluciones

de las ecuaciones diferenciales indicadas.

= 2 +1

3 + 2 =

= 2 + 1 2 1 2 + = 2

=

0

+ =

3

ECUACIONES DE VARIABLES SEPARABLES

1 2 + 1 2 = 0 . 1 2 + 1 2 = 1; = 1

4

1 +2

ln = 0 . +

= ln ln

5

2 2 + 1 + 2 2 + 2 + 2 2 + 2 = 0

. 2 2 + 2 2 + 1 2 tan =

6

3

= 4 + 1 . ln 4 + 1 = + 4 sin

7

=

1 5

2 23 .

1

33

2

=

1

+ ln +

8

2 = 1 2 + 2 22 . = tan 1

9

= 1 + + + . ln 1 + = +1

22 +

10

ECUACIONES HOMOGNEAS

4 3 + 2 3 = 0 . 2 3 + 22 =

11

42 + 2 + 2 + 42 = 0 . + 3 + 3 =

12

=2

32 2 . 2 2 = 3

13

cos

+ cos

= 0 . = sin

14

2 2 = 2 . = 2 + 2

15

= 2 + 42 + 2 . 42 + 2 = 2 ln + 2

16

= + 2 + 2 . + 2 + 2 = 2

17

+ = 2 + 2 . 2 + 2 =

18

+ + 3 + = 0 . 2 2 + 2 =

19

= + + 1 . = 2 + + 1 2 ln 1 + + + 1 +

20

ECUACIONES EXACTAS

sin 2

+ +

2

2 = 0 .

2

+2 + 2

2=

21

+

2 + 2+

2= 0 . 2 + 2 +

=

22

2 + 3 + 3 + 2 = 0 . 2 + 3 + 2 =

23

4 + 6 = 0 . 22 + 32 =

32 + 22 + 4 + 62 = 0 . 3 + 22 + 23 =

24

22 + 32 + 22 + 43 = 0 . 3 + 22 + 4 =

3 +

+ 2 + ln = 0 . 34 + 43 + 12 ln =

25

FACTOR INTEGRANTE

2+ 2 +

1

1 + ln = 0 . ln + 2 =

26

1

2 1 + ln +

3 3 = 0 . ln 3 =

27

32 2 + = 0 . = 3

+1

3

2 + 2 = 0 . 2 = 2 2

28

2+ 22 + 42 = 0 . 24 +

2

2=

29

ECUACIONES LINEALES

3 + 1 + 23 1 =3 2

. =

3 + 1+

1

30

+ = . = 1 +

31

2 = 32 + 2 . = 32 ln 2 + 2

32

+ 4 = 95 + 23 . = 5 +2

73 + 4

33

+ 4 = 3 . =5

25 2 + 3

34

+ ln = ln . = 1 + 1ln

35

8 = 1

3 + 1 . 4 = + + 1

36

ECUACIONES DE BERNOULLI

3 2 =3

2 . 3 = 2 + 3

37

+1

=

2

344 .

1

33+ 2 =

38

+ = 2 . 3 = 1 + 32

2

39

+1

= 431 . 2 =

4

34 + 2

40

= 21

2 . = 2

4 + 2

41

3 2 = 32 . 3 3 = 2