- - -
: y' - 2 * y = 4 * x + 1 >
> >
!!!
!!!
y` 2y = 4 x+1
y(x) = u(x)v(x)
y` = u`v + uv`
u`v + uv` 2uv = 4 x+1
u`v + u(v` 2v) = 4 x+1
v` - 2v = 0,
dv/dx - 2v = 0
dv/v = 2dx

???? , .
smile.gif
, - ((((
:
:
∫ dv/v = ln│v│+ C = ln│x│+ C
∫ 2dx = C
= 0 → ln│x│+ C = lnx
v = x, :
u`v + u(v` 2v) = 4x +1
u` + u(` 2) = 4x +1
u` + u` 2u = 4x +1

, . ,
Black Ghost
∫ 2dx = 2x+C
ln│v│=2x+C
C=0
ln│v│=2x
v=e^(2x)

u`v + u(v` 2v) = 4x +1
v` 2v=0

u`v = 4x +1
v=e^(2x), u`e^(2x) = 4x +1
u` = 4xe^(-2x) +e^(-2x)
u = ∫ (4xe^(-2x) +e^(-2x))dx =...
..... . (((
u = ∫ (4xe^(-2x) +e^(-2x))dx = 2x^2 + 4C + 2e^(-2x) + 2C = 2x^2 + 2e^(-2x) + 6C
y = uv = (2x^2 + 2e^(-2x) + 6C) e^(2x) =

,
Black Ghost
.
Teleglaz
, !

.

Q-2=0
Q=2

Y=C1*exp(2*x).
.. - - Y = (a1*x+a2), 1 2 . .
Y` = 1.
a1-2*a1*x-2*a2=4*x-1
:
(I) -2*1=4
(II) 1-2*2=1
=>a1=-2, a2=-3/2.

Y = C1*exp(2*x)-2*x-3/2
!
(Teleglaz @ 18.6.2007, 12:26) *

, !

.

Q-2=0
Q=2

Y=C1*exp(2*x).
.. - - Y = (a1*x+a2), 1 2 . .
Y` = 1.
a1-2*a1*x-2*a2=4*x-1
:
(I) -2*1=4
(II) 1-2*2=1
=>a1=-2, a2=-3/2.

Y = C1*exp(2*x)-2*x-3/2
!

, , .. . , . .
wils
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