"
"
d2y dy
a + b + cy = f(x), (a = 0).

dx2 dx
y f
x a, b, c
f(x) a" 0
y1(x, C1, C2)
y2(x)
y = y1(x, C1, C2) + y2(x).
ar2 + br + c = 0 (a = 0),

d2y dy
a + b + cy = 0, (a = 0),

dx2 dx
y = erx.
ar2 + br + c = 0 (a = 0).

 ´ = b2 - 4ac > 0
r1 r2
1 2
y = C1er x + C2er x.
´ = b2 - 4ac = 0
r
y = (C1x + C2)erx.
´ = b2 - 4ac < 0
r1 = Ä…+²i r1 = Ä…-²i
y = eÄ…x(C1 cos ²x + C2 sin ²x).
2y - 5y - 3y = 0
4y + 12y + 9y = 0
y + 4y + 13y = 0
CORN = CORJ + CSzRN.
CORJ
CSzRN
y - 4y + 4y = 8x3 - 36x
y + 4y = sin 3x
1
y - y = 2x cos x + ex x = 0 y = y = 1
2