2 3 HW
.
3
dy
-B +-D 0 Linear
-tct
=
.
Both linear & separable
+ Inty
et
dt
4
.
dy
dt
Enty
=
31 > Linear
=
-
>
-
et
Unseparable
Linear
-
12
,
1
+4
.
.
2
P(x) = 4
w(z)
-
Q (x) = x 22
,
e
=
xe 4x
=
-
*. They are defined over 1-0 c)
4
,
.
5 P(x)dx+C
p(s) = 24
*
.
3
* [e
*
·
y(x)]
/f
=
2**. xe
=
x2
-
*
g) is Ee
↳
.
14
1
x +By Sinx 3
+ y Sne-3x
=
.
-
=
2
.
P(x) = -, Q(x)
M(z) = eS
=
.
3
=
.
S-32
They are und. at x
=
plux
=
x
Siesincedi
=
* [x3 y]
=
x3(2 3x)
=
/9
=
usinx - 3x4
=
4 x3 Y
.
1/
y=
-
=
Sxsinze dx-
=
-
.
+ C
xcosse-sins5
+ -I t i
L
-
0
.
I = 1
-
4,
0) U /0 b)
,
.
Plaidx + C
e3lnx
.
=
UV-Jude
>rosx-S-cosse dx
-
-
xcosse + sinze
n=x
di = I dx
due be as
24
.
Y2lt) sin (et)
Because
costsint
=
=
2y It)
Y2(t)
=
.
,
.
.
they are linearly dependent
.
28
linearly dependent
est = ke-4t if
k
1) e
=
1
.
10 1) that satisfies
in
,
.
.
if 1 c
test = ke't
k
No value of t
.
linearly independent
so
29
+ =
.
t) text= teit
=
,
.
but t is not a constant
.
.
linearly independent
So
.
30
tcos(Int)
=
KEsin(Int)
Equation above is true only if t
so linearly independent
=
0
.
.
31
.
tanit-sect
=
3K
* sect-tanit = 1
-
1 = 3K
.
K
.
= .
K is
constant, so
linearly dependent
.
32
0 = Ket ,
K
=
0
K is a constant
,
so
linearly dependent
.
.
But
OCt < 1
.
equation
.