pdf (it, 2.898,97 KB, 25/01/13)

M(x, y) dx + N(x, y) dy = 0
1
M, N Mx+Ny = 0
Mx + Ny
x dy − y dx
x dy − y dx
x dy − y dx
x dy − y dx
x dy + y dx
x dy + y dx
1
x 2
1
y 2
1
xy
1
x 2 + y 2
1
(xy) n
1
(x 2 + y 2 ) n
y
d
x
d − x
y
d ln y
x
d arctan y
x
⎧
⎪⎨
d(ln(xy)) n = 1
⎪⎩
1
d −
(n − 1)(xy) n−1
n = 1
⎧
1
⎪⎨
d
2 ln(x2 + y 2
)
⎪⎩ d −
1
2(n − 1)(x 2 + y 2 ) n−1
n = 1
n = 1
λω = 0
P (x0, y0) ∈ D N(x0, y0) = 0
dy y)
= −M(x,
dx N(x, y)
P λω F
F ∂yF (x0, y0) = λ(x0, y0)N(x0, y0) = 0 F
P (x0, y0) y = y(x) y0 = y(x0) M, N ∈ C 1
λ = 0 N(x, y) = 0 P (x0, y0)
y = y(x) C 1
dy y)
= −M(x,
dx N(x, y) .
M(x0, y0) = 0
dx
dy
= − N(x, y)
M(x, y)
P
y ′ = f(x, y)
f(x, y) dx − dy = 0.