Ecuaciones Diferenciales
Páginas: 2 (362 palabras)
Publicado: 9 de diciembre de 2012
1) (x-y)dx+xdy=0
+
=0
=0
U= -
Y=-ux
dy= -xdu-udx
[x-(-ux)]dx+x(-xdu-udx)=0
-
=0
- u=c
=
2) (x+y)dx+xdy=0
U=xy Y=
dy=
(x +)dx+x(
+ u=c
)=0
dx+
+xy=c
=0
y=
y=
+
=0
y=
3) Xdx+(y-2x)dy=0
Xdx+(ux-2x)(xdu+udx)=0
Xdx+u
(x+
xdx-2
x-2xu)dx+(uX(1-2u+
x
du+
)dx+
-2
du+2xdx=0
du)=0
(u-2)du=0
=c
=c
4) Ydx=2(x+y)dy
Y=ux dy=xdu+udx
u=
Uxdx – 2(x+ux)(xdu+udx)=0Uxdx-2
du-2xudx-2u
du-2
xdx-uxdx-2
xdx-2
du-2u
du=0
5) (
Y=ux
dy=xdu+udx
u=
[
0
[
dx – [
=c
=0
y=
y=
6) ( Y=ux
dy=xdu+udx
u=
[
0
(
0
0
0
0
7)
(y-x)dx – (y+x)dy=0
Y =ux dy=xdu+udx u=
(ux-x)dx-(ux+x)(xdu+udx)=0
Uxdx-xdu-u
du--x(1+
(u+1)du=0
)dx-
xdx-
du-uxdx=0
du=0
0
8)
Y =ux dy=xdu+udx u=
(x+3y)dx=(3x+y)dy
(x+3y)dx-(3x+y)dy=0
[x+3(ux)]dx-[3x+ux](xdu+udx)=0Xdx+3uxdx-[3
-x(
-1)dx-
du+3xudx+u
(3+u)du=0
du+
]
0
9) –ydx+(x+
dy=0
Y =ux dy=xdu+udx u=
-uxdx+(x+
-uxdx+
)(xdu+udx=0du+xudx+
du+x dx=0
0
10) x
x>0
xdy-(y+
)dx=0
Y =ux dy=xdu+udx u=
X(xdu+udx)-(ux+
du+xudx-(uxdx)-x
=c
)dx=0
=c
dx=0
=0
11) xy(1)=2
/2
1+16=c
c=1
P(x)=-
12)
y(-1)=1
Y =ux dy=xdu+udx u=
c= -0.23
13)
y(1)=0
Y =ux dy=xdu+udx u=
c=1
14) Ydx+x(
-1)dy=0y(1)=e
Y =ux dy=xdu+udx u=
Uxdx+x(
Uxdx+
-1)(xdu+udx)=0
(
-1)du+xu(
-1)dx=0
Uxdx+
Xu[
15) x
xu=x+c
u=
16)
y=
-u=
+
=0
=0
U= -
Y=-ux
dy= -xdu-udx
[x-(-ux)]dx+x(-xdu-udx)=0
-
=0
- u=c
=
2) (x+y)dx+xdy=0
U=xy Y=
dy=
(x +)dx+x(
+ u=c
)=0
dx+
+xy=c
=0
y=
y=
+
=0
y=
3) Xdx+(y-2x)dy=0
Xdx+(ux-2x)(xdu+udx)=0
Xdx+u
(x+
xdx-2
x-2xu)dx+(uX(1-2u+
x
du+
)dx+
-2
du+2xdx=0
du)=0
(u-2)du=0
=c
=c
4) Ydx=2(x+y)dy
Y=ux dy=xdu+udx
u=
Uxdx – 2(x+ux)(xdu+udx)=0Uxdx-2
du-2xudx-2u
du-2
xdx-uxdx-2
xdx-2
du-2u
du=0
5) (
Y=ux
dy=xdu+udx
u=
[
0
[
dx – [
=c
=0
y=
y=
6) ( Y=ux
dy=xdu+udx
u=
[
0
(
0
0
0
0
7)
(y-x)dx – (y+x)dy=0
Y =ux dy=xdu+udx u=
(ux-x)dx-(ux+x)(xdu+udx)=0
Uxdx-xdu-u
du--x(1+
(u+1)du=0
)dx-
xdx-
du-uxdx=0
du=0
0
8)
Y =ux dy=xdu+udx u=
(x+3y)dx=(3x+y)dy
(x+3y)dx-(3x+y)dy=0
[x+3(ux)]dx-[3x+ux](xdu+udx)=0Xdx+3uxdx-[3
-x(
-1)dx-
du+3xudx+u
(3+u)du=0
du+
]
0
9) –ydx+(x+
dy=0
Y =ux dy=xdu+udx u=
-uxdx+(x+
-uxdx+
)(xdu+udx=0du+xudx+
du+x dx=0
0
10) x
x>0
xdy-(y+
)dx=0
Y =ux dy=xdu+udx u=
X(xdu+udx)-(ux+
du+xudx-(uxdx)-x
=c
)dx=0
=c
dx=0
=0
11) xy(1)=2
/2
1+16=c
c=1
P(x)=-
12)
y(-1)=1
Y =ux dy=xdu+udx u=
c= -0.23
13)
y(1)=0
Y =ux dy=xdu+udx u=
c=1
14) Ydx+x(
-1)dy=0y(1)=e
Y =ux dy=xdu+udx u=
Uxdx+x(
Uxdx+
-1)(xdu+udx)=0
(
-1)du+xu(
-1)dx=0
Uxdx+
Xu[
15) x
xu=x+c
u=
16)
y=
-u=
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