Intro
.1
3
order
State the
+
-
second
order
ty" Ey"
·
-
second order
05
,
matching
Determine
equ
it with (6)
·
whether
.
cosk
linear
+
by
=
0
non-linear
de
.
second order
07
.
non-linear
-
sin
.
,
(sino y" (2000) y
third order
04
,
=
DE
ordinary differential
nonlinear by
or
(l-x) " Yxy' By
d
03
linear
is
the equi
the given
of
to
Verify
,
that
-
y
y
y
-
y"-by
=
=
=
=
=
e+
x
non-linear
the
differential
egn
R 15
2
linear
,
(dy/dx)
first order
=
+
·
explicit sol of the given
appropriate interned I of def for each sol.
indicated function
Assume
13 y
=
0
;
an
y
=2
is
coshx
ecos2x
Je cost-e · Isind
3e"cos2x-Lesinde
-e (Isindx-3cos2x)
an
I
"
-dax [
=
**
"
I
y
"
=
y
-"
=
-
(2sin2x
-
3 c032x)]
(Isindx-3c0s2x)
[3e(Isinhx-3coshe)
-
=
y
y
[32
-
*
[Je"(2sinIx-3cosha)
**
[be sinds-9e"costa
-
**
=
[12e
-
y" -by'
+
Since
By
-
+
+
23 (2ddx(sin2x)
+
e
+
=
e
*
[2 2 cos2x-3
.
"(42062x
Ye "costal
+
.
34/ax(cos2x))]
-
-2sinkx))
6sin2x)]
be"sinar]
+
5e""costx]
0
=
[-e (Isindu-3cosha)) + 13/e cos2x)
ostetos2x 0
Sindet stating
(I2sin2x -Joshe)
- e
-
*
6
*
=
0
=
=
: .
0
indicated function is
The
verity
an
explicit sol
that the indicated Function
y
=
given first-order DE Consider Of simply
Then consider o as a sel of the DE
.
,
09
=
2x
;
m
=
+
u
y
as
a
an
.
,
one
This is indeed the
Function
explicit sol of
function
atleast
give
X
zey
4 x
-
=
02)
1/2x)
-
(1 x2)2
-
y
x2
(x) is
shown
its
implicit
The domain
=
2x
-
16
y
-
-
8x2 + x4
=
x
x
-
0
= Y
x
=
12
y
the
domain
give
internal I of def.
is
sol
Edsize
=
onatee
=
-=
Data=
.
of
the
(KER/x + =2)
-
=
i
-
:
as
Y
-
x2
verify
025
·
that the
functions
Ey 4 Ay
y" Yy'
-
+
Yy
=
are
=
y"
y
0
=
y
0
=
=
Ye + Ylze + Yakem
=
422x(
"
(2
+
+
=
C , e"
.
DE
i
+
Lee
Care
2caxe (1)
2 Ce
C
Ye + 2G* + Ylaxe
=
y
;
=
-
,
of the given
*
+
y
y
-"
sal
a
,
e+
+
(2)
,
+
222x +
+
2)22x
Ice
+
(2x)
y
y -My
1462-4lze Yes )-4(2 ethlake + Ge + 4 (Ge+ Laxe )
+
=
0
*
+
use
/
=
·
+
4
,
zx
-Y tipe
-e -
O
The
function
is
indeed
a
set
of given
DE
=
O
=
0