April 8, 25
MAT120
(hapten 2:3
Find the solutisn of tue qiven
DEG
5y
- 5y
3
Inegratmg
P( da
Pt
factor ( I . £ ) : J
esda
5
Nev
dy.
fntegeting
52
5e
y
both sides
-SA
.y
ee
(ns)
0, e
-Sx
Heru, PC
Pc
= oeficient ofy
. . P(«)- 5
x4
(2)
+ (3x +1) : e
maltplying/div idiny Lota sides
by t
(if divide len x)
(3e1)y
Trtegnating facton (I.F.)
e
e'
Here P( )
(3+*)
3a
Now,
standand ongm
the
with
|I.f)
multi py ing
(e 1)
(#e)
(aey )
Solve the given initial value problum (4vP) :
dn
dy
dividing botth sides by
dy
y
2y
(1):
y
24
2y
which is tue
Integrating faclon (TF)
standard
Here py) e
=
e-lny
en y
Now,
low,
F) x en eqatien t
a
of
of slandared
fonm by (I.F)
muttiply ing both sides
form
.
dy
f2 dy
Giyen that
Here
eg ( )
49
S:
input vale of
2y -
wz Next
2·4
7C
Ezat Equa lions
Hue
A finst or den
said to be
is
2)
form
eacB if te
follow ing
f'ondi- ion
sattfied
M
Necessany
ON
M,N
and
condition,
2xy da + (x°- 1)dy
Solve
Here,
Sol:
M
o
22y
24
N
OM
So
given
Here,
N( ) e 2t.
exaet
sutfient
Indegnating eation 4
f(«o)
2y
2
+
(4) + a' Cy)
v
)
(ompaning
*-1 = x" t + g' ty) .
Indegrating both sides
4
New
ey ( )
’
yxtl-),
(ans )
(eoy
dn
t(27
2y
N
2y)dy -0
2x e?-
(osyt
M
2e
•N
2y
2e?cosn -*y
(- sin ny )3
2,,eorny
2e2y
eaact
4he given
Here
Ma)
24 e 2y
Integratin
Cu)
e