Matemáticas Discretas

Tarea S4
1.- (2x-1) dx + (3y+7) dy =0
M(x,y)= 2x-1 ; N(x,y)= 3y+7
= 0 = 0
F(x,y)= 2x-1
= 2 - + g(y)
F(x,y)= x2-x+g(y)
g’(y)= 3y+1
= 3 + + C
g(y) = y2 + y +C
x2 – x + y2 +y =C
Soniguales es Exacta.

2.- (5x + 4y) dx + (4x -8y3) dy =0
M(x,y)= 5x + 4y; N(x,y)= 4x -8y3
= = 4
= = 4
Son iguales es Exacta.

3.- (2y2x -3) dx + (2yx2 +4) dy = 0
M(x,y)= 2y2x -3 ; N(x,y)=2yx2 +4
= = 4xy
= = 4xy
Son iguales es Exacta.


4.- (x + y) (x – y) dx + x(x-2y) dy =0
(x2 – y2) dx + (x2 – 2xy) dy = 0
M(x,y)= x2 – y2 ; N(x,y)= x2 – 2xy
= = -2y
= = 2x – 2y
Noson iguales, No es exacta.




5.- (2y - + cos 3x) + – 4x3 + 3y sen 3x = 0
( – 4x3 + 3y sen 3x) dx + (2y - + cos 3x) dy = 0
M(x,y)= – 4x3 + 3y sen 3x ; N(x,y)= 2y - + cos 3x
= = + 3sen 3x
= = - 3 sen 3x
No son iguales, No es exacta




Tarea S5
Resuelva las siguientes Ecuaciones Diferenciales Exactas:
1.
F(x, y) = + g(y)
= x3 + 2x2y + g(y)
=
g’(y) = 2y
g(y)= = y2
F(x, y) = x3 + 2x2y + y2 + C

2.-
F(x, y) = dy + h(y)
= + h(y)
= + h’(x)
h’(x) = -
=
h(x)= +
F(x, y) =

3.-
F(x, y) = dx + g(y)
= + g(y)
= g’(y)
g’(y) = 3y + 7g(y) = = + 7y
F(x, y) = + 7y = C

4.-
F(x, y) = dy + h(x)
= -2x4 + h(x)
h’(x) =
h(x) = = + 4xy
F(x, y) = + 4xy -2 + C

5.-
F(x, y) = dy + h(x)
= y + - + h (x)
= - y +h’(x)
h’(x) = sen x – sen y – y sen x
h(x) = = (y-1) cos (x) – x sen (y)
F(x, y) = (y-1) cos (x) – x sen (y) + y + -
Determine el factor de integración de las siguientes ecuaciones yposteriormente resuélvalas.
1.-
= 4y
= 2y
= = = = = = x


F(x, y) = dy + h(x) = + h(x)
= + h’(x)
h’(x) = = 3
h(x) = =
F(x, y) = +

2.-
= 6y
= 18y

= = = = = =
12x dx +(8 + 18 y) dy = 0
F(x, y) = dx + g(y) = + g(y)
= + g’(y)
g’(y) = 8 + 18 y + = 8 +
g(y) = = +
F(x, y) =

3.-
= 6
= 0
= = =
(10 – 6y +1) dx - 2dy = 0
10 dx – 6y dx+ dx...