1. No category

(C) "
-
-
'
'
2
xy' ' (1 2 x) y '
y' ' 3 y'
2x 2
x 2 y" xy ' y
y1
x
(C) "
-
-
'
'
2
0
"(I) ay" (t ) by ' (t ) cy (t ) g (t )
#
a,b,c
%
g a $0
(I)
"
g
%
(C) "
-
-
'
'
2
!
2 y" (t ) 3 y ' (t ) 5 y (t ) 0
y" (t ) 5 y ' (t ) y (t )
2 sin t t
x 2 y" xy ' 2 y
(C) "
-
e2 x
-
'
'
2
&
(
(
(C) "
-
-
'
'
2
'
*
*
+
+
R
(C) "
"(I)
%a 0
-
-
'
'
2
)
ay" (t ) by ' (t ) cy (t )
0
a,b,c
%
(I)
(II)
ar 2
br
c
0
b2
(C) "
-
-
'
'
2
y" 5 y ' 6 y
(C) "
4ac
,
0
y" 7 y ' 10 y
0
2 y" 3 y ' 5 y
0
-
-
'
'
2
-
y" 2 y ' y 0
4 y" 4 y ' y 0
(C) "
-
-
'
'
2
.
y" y ' y 0
y" 2 y ' 5 y 0
(C) "
-
-
'
'
2
ay" by ' cy
y (t 0 )
ay" by ' cy
y (t0 )
(C) "
!
-
-
0
, y ' (t0 )
'
, y (t1 )
'
2
0
, ,
, ,
R
R
(
(
(C) "
-
-
'
'
2
+
(I)
ay" (t ) by ' (t ) cy (t )
(C) "
-
-
'
'
g (t )
2
!
+
yp(t) +
*
%
"
+
(C) "
&
-
-
'
'
2
&
from: R. Nagle and E. Saff:
Fundamentals of Differential Equations, Addison-Wesley
(C) "
-
'
'
2
y" 2 y ' 3 y
2x
y" 2 y ' 3 y
y" 2 y ' 3 y
x
+
+
sin 2 x
y" 2 y ' 5 y
e x sin 2 x
(C) "
-
-
'
'
+
2
)
+
v2
/
(C) "
'
'
e
cos x
e2 x
y" 5 y ' 10 y
y" 4 y
-
-
-
'
'
v1
2
,
+
+
(C) "
-
-
'
'
2
+
-
+
t
y" 2 y ' 1 e
y" 5 y ' 6 y e
y" 9 y sin 3t
y" y
(C) "
-
-
'
'
2t
tan x
2
.
Superposition principle
y" 5 y ' 6 y
t sin t
y" 4 y ' 4 y
e
(C) "
)
-
-
'
'
2t
2
cos t