"
"
"
"
F (x, y, y ) = 0,
y x y
1
y = 2xy2 - xy , x2y = sin , y = 2y.
x
y = Õ(x),
x
y = È(x, C),
C
C
y = 2y
y = Ce2x,
C C
-3, 0, 1, 5
y = -3e2x, y = 0, y = e2x, y = 5e2x.
 (x0, y0) C0
C
y0 = È(x0, C0).
C0
y = È(x, C0).
x = 0 y = 4
x = 0, y = 4 C0 = 4
y = 4e2x.
C
dy
p(y) = q(x).
dx
p(y) y p(y) = 0

q(x) x
(x, y) (x1, y1)
y = f(x) f

y x
p(·)d· = q(¾)d¾.
y1 x1
dy 1
x2 = sin
dx x
2
dy
sin2 x + = 1
dx
dy dy
= 2xy2 - x2
dx dx
dy
sin x = y cos x
dx
dy
+ p(x)y = q(x),
dx
y y
q(x) a" 0 y y
dy
+ p(x)y = 0
dx
y = Ce-P (x),
P (x) p(x) C
dy 1
= y
dx 3x
dy 2x - 1
= y
dx x2
dy
= y tan x
dx
dy
+ p(x)y = 0
dx
dy
+ p(x)y = q(x)
dx
= + .
dy
+ p(x)y = q(x)
dx
y = C(x)e-P (x),
C(x) x P (x)
p(x)
dy 2
- xy = xex
dx
dy
x - y = 2x3
dx
dy
sin x + y cos x = sin 2x
dx
dy
x - 2y = x3 cos x
dx
y + ay = becx,
a, b, c " R
y = mecx,
m
dy
- 2y = 2e3x
dx
dy
- 4y = 2e4x
dx
y + ay = Wn(x),
a " R Wn(x) n
n
dy
+ 2y = x2
dx
dy
- 2y = 3x2 - 2x3
dx
y + by = c sin ax + d cos ax,
a, b, c, d " R
y = m sin ax + n cos ax,
m, n " R
dy
+ 2y = 5 cos x
dx
dy
+ y = 5 sin 3x
dx
y - 2y + 3 = 0
(0, 1)
y - 5y = e5x
(1, e)
5
y + y = sin x
1
(Ä„, )
2
dy
- y = xe2x
dx
dy
+ y = 2x sin x
dx
dy
- 2y = 6(cos 2x - sin 2x)e4x
dx
dy
+ p(x)y = q1(x) + q2(x)
dx
dy
+ p(x)y = 0
dx
dy dy
+ p(x)y = q1(x) + p(x)y = q2(x),
dx dx
= + + .
1 2
dy
- 2y = 6 cos 2x - 2 sin 2x + x - 2x3
dx
dy
+ y = (x + 1) sin 3x + 3x cos 3x + x2 - 2 + 2xe-x
dx
dy
+ p(x)y + q(x)yn = 0,
dx
p(x) q(x) n
 n = 0
n = 1
y y
n > 0 y = 0
y1-n = z
y + y + y2 sin x = 0
"
y + y + x y = 0