Edolineales1orden 150313183417 Conversion Gate01
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y =f(x, y)
y(x)
y(x)
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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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(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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dydx = ay + b
(4)
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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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y 2y= 0
dy
dx= 2y
y = 0 y
1
y
dy
dx= 2
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dx
dy
y = 2dx
c dy
y = 2
dx
|y| =e2x+C =ece2x =C1e2x
C1=e
c
y(x) =C1e2x
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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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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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y =x
y
y = 1
xy3
y =x3
y2
xy =y 1
xy +y =y2
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y
+ay =b
a= r b=k y= (b/a) +ceax
y= (k/r) +cerx
y ry =k; r = 0.
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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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xy 2y =x5
ep(x)dx
ep(x)dx
y(x)
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y +p(x)y =q(x)
xy 2y=x5
1/x
y
2
x y =x
4
p(x) = 2
x
q(x) =x4
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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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ep(x)dx
x2
(x2)y 2x (x2)y= (x2)x4
x2y 2x3y=x2
(x2y) =x2
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y(x)
(x2y) =x2
(x2y) =
x2dx
x2y= x3
3 +C()
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y(x)
()
y=Cx2 +x5
3
C
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y
3y=e2x
y + tan (x)y = sin 2x
y +xy =x3
dxdt
+x= e2t
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y +p(x)y =q(x)
(x)
(x)y +(x)p(x)y=(x)q(x)()
(x)y
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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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()
[(x)y] =(x)q(x)
(x)y=
(x)q(x)dx+c
c y
y= 1
(x)
[ (x)q(x)dx+c]
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(x2
+ 1)y
2xy=x3
+x x2y + 4xy= 2
x
y x2y= 4x2
y 11y= 4e6x
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(1546 1642)
dv
dt = g;
v
g
t0
v0
dv=
tt0
gdt
2da
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2da
v(t) =v0 g(t t0)
2da
mdv
dt =
f;
2da
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2da
ag fr
f=ag+fr
mdv
dt
= f= mg v
dv
dt = g
mv
dv
dt +
mv= g
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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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4kg
12v v
m/s
v(t)
y(t) t
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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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T(t)
dTdt
Tm
dT
dt = k(T Tm)
k >0
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Tm = 20C.
100C 60
20
30
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dT
dt = k(T Tm); )
dT
(T Tm)= k
dt+C ln |T Tm| = kt+ ln C
T =Tm+Cekt
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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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x(t)
t
dx
dt =R1 R2
R1=
R2=
R1=q1c1; R2=q2c2
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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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4l/min
2l/m
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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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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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v0= 100m/s.
v1= 80m/s. b= 0,1m
R=v2
.
T
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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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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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(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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