Edolineales1orden 150313183417 Conversion Gate01

7/24/2019 Edolineales1orden 150313183417 Conversion Gate01

1/49

1

1
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2/49
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3/49
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4/49

y =f(x, y)

y(x)

y(x)
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5/49

a(x)y +b(x)y=C(x)

y

ax1+by1=c a(x), b(x), C(x)

C(x) = 0
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6/49

(2)

y +p(x)y =q(x)

(3)

p(x) =a; q(x) =b a b y +ay =b

y = ay+b
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7/49

dydx = ay + b

(4)
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8/49

dydx = ay + b

dy

dx= ay+b

dy/dx

y ( ba

)= a

a = 0

y=

b

a

ln |y (b

a)| = a+C

y= (b/a) +ceax
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9/49

y 2y= 0

dy

dx= 2y

y = 0 y

1

y

dy

dx= 2
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10/49

dx

dy

y = 2dx

c dy

y = 2

dx

|y| =e2x+C =ece2x =C1e2x

C1=e

c

y(x) =C1e2x
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11/49
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12/49

y +p(x)y=q(x)

y =dy/dx= f(x, y)

f(x, y) =g(x)/h(y)

p(y) = 1/h(y)

dy

dx=g(x)p(y) =

g(x)

h(y)
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13/49

h(y) (5)

h(y)dy=g(x)dx

h(y)dy=

g(x)dx

H(y) =G(x) +C H(y) h(y) G(x)

g(x) C
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14/49

y =x

y

y = 1

xy3

y =x3

y2

xy =y 1

xy +y =y2
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15/49


16/49

y

+ay =b

a= r b=k y= (b/a) +ceax

y= (k/r) +cerx

y ry =k; r = 0.
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17/49

y +p(x)y=q(x) p(x) = r q(x) =k

(x) =erdx =erx

(x)

(x)y (x)ry =(x)k

y= 1

erx(

erxkdx) =erx(

k

r erx +C) = (k/r) +cerx
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18/49

xy 2y =x5

ep(x)dx

ep(x)dx

y(x)


19/49

y +p(x)y =q(x)

xy 2y=x5

1/x

y

2

x y =x

4

p(x) = 2

x

q(x) =x4


20/49

ep(x)dx

p(x) = 2

x

ep

(x)dx

=e2 dx

x

e2 dxx =e2 ln |x| =x2

e2 ln |x| =eln |x|2

=x2
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21/49

ep(x)dx

x2

(x2)y 2x (x2)y= (x2)x4

x2y 2x3y=x2

(x2y) =x2
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22/49

y(x)

(x2y) =x2

(x2y) =

x2dx

x2y= x3

3 +C()
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23/49

y(x)

()

y=Cx2 +x5

3

C
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24/49

y

3y=e2x

y + tan (x)y = sin 2x

y +xy =x3

dxdt

+x= e2t
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25/49

y +p(x)y =q(x)

(x)

(x)y +(x)p(x)y=(x)q(x)()

(x)y


26/49

d(x)

dx =(x)p(x)

d(x)/dx

(x) =p(x)

ln (x) =

p(x)dx+K

(x) =ep(x)dx
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27/49

()

[(x)y] =(x)q(x)

(x)y=

(x)q(x)dx+c

c y

y= 1

(x)

[ (x)q(x)dx+c]


28/49

(x2

+ 1)y

2xy=x3

+x x2y + 4xy= 2

x

y x2y= 4x2

y 11y= 4e6x
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29/49
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30/49

(1546 1642)

dv

dt = g;

v

g

t0

v0

dv=

tt0

gdt

2da
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31/49

2da

v(t) =v0 g(t t0)

2da

mdv

dt =

f;

2da
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32/49

2da

ag fr

f=ag+fr

mdv

dt

= f= mg v

dv

dt = g

mv

dv

dt +

mv= g
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33/49

q(x) = g p(x) = m

(x) =e mdt

v(t) =cemt

mg

()

t0 v0 c

v0=ce mt0

mg

c

()

v(t) = (v0+mg

)e

m(tt0)

mg
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34/49

4kg

12v v

m/s

v(t)

y(t) t
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35/49

mdv

dt = f=F1 F2

m= wg

= 410 = 25 ; F1= 4; F2=

12v

2

5

dv

dt = 4

1

2v

y(0) = 0

v(t) = 8(e5

4t 1);

, y(t) =

32

5e

5

4t 8t

32

5
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36/49

T(t)

dTdt

Tm

dT

dt = k(T Tm)

k >0
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37/49

Tm = 20C.

100C 60

20

30


38/49

dT

dt = k(T Tm); )

dT

(T Tm)= k

dt+C ln |T Tm| = kt+ ln C

T =Tm+Cekt
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39/49

t= 0

T= 100C

100 = 20 +Cek0 = 20 +C C= 80

t= 20 T = 60C

60 = 20 +Cek20 k= 1

20ln

60 20

80 = 0,03466

T= 20 + 80ek0,03466t t= 1

0,03466ln

T 20

80

T = 30

t= 10,03466

ln30 2080

= 60

60 20 = 40

30
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40/49

x(t)

t

dx

dt =R1 R2

R1=

R2=

R1=q1c1; R2=q2c2
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41/49

q1= c1=

q2= c2=

xV

x=x(t) V =V(t)

t

q1=q2

q1> q2

q1< q2

V =V0+ (q)t q=q1 q2
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42/49

4l/min

2l/m
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43/49

dA

dt =R1 R2

R1= (4l/m)(1gr/min) = 4gr/min

R2= (2l/min)(Agr/l) = 2Agr/min V t

2l/min

tf =

=2002 min= 100
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44/49

R1

R2

dA

dt = 4

A

t+ 100; A(0) = 30

A(t) = 2(t+ 100) + C

t+ 100; 0 t 100

C= 17000

A(t) = 2(t+ 100) + 17000t+ 100

A(100) = 315
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45/49

v0= 100m/s.

v1= 80m/s. b= 0,1m

R=v2

.

T
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46/49

ma=

F : mdvdt

= v2

dv

v

2 =

m

dt+C= 1

v

=kt+C

k= m

C

t= 0, v =v0 C= 1v0

1

v =kt+ 1

v0 = v=dx

dt = 1

kt+ 1v0
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47/49

t

x= 1

kln

kt+

1

v0

+C1

C1

t= 0, x= 0 C1= 1k

ln 1v0

x= 1

k

lnkt+ 1

v0

1

k

ln 1

v0
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48/49

(7) t= T , v =v1

1

v1=kT+

1

v0

(9) t= T; x= b :

b= 1

kln

kt+

1

v0

1

kln

1

v0= k=

1

bln

v0v1

(10)

T = 1

k

1

v1

1

v0

=b

1v1 1

v0

ln v0v1

= 0,1 180

1100

ln 10080= 0,000819s
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49/49
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Date post:	20-Feb-2018
Category:	Documents
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Edolineales1orden 150313183417 Conversion Gate01

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