PDE
System Of ODE
Handwritten Notes
By Sanjibon Hazarika
,D:eretia OpeoTor omod operato athad
malhod
The Gmenal imer syslem
two firu ortdlo DE two
ww known wnetions
+he om
a,(t) + alt) a,(t)x + a,lt)y - F )
b(t) dt
,)+bt)
dt +b,=F
V
2 2 dL3 2x+
= t
d -2 +3+
We shall that soltionn
s O
euot ion OO O orolarad palr
o
mafios gsweh that
of
- 4 (t)y- Simultoma.ous
sst
both e o Hho sytem O o
somo Ral indaLvod a t b
, Tho gemera meas stem
thora t ordloru DE thraa wnknowh
wnctians mc z
or
a,4)ax
+a)a9+a,6)+ ag) *
at) z = F()-
t
b,t)z Ft)
c,e) Cc)+ +e,(0x +)y+|
e
d-2+d
t+
+2-
3-z -t
lt d5 +4y - 5z =
Sint
d 2 + - 3 +2y
-Z =eot
dt
, Asol stemD
rao unefion
orolarad frupa e
(+,3, sueh hat - {lt), Fg
ound z=
ht) Simutamaosly
euaton
tha Syslem
SomO roal intaruva& atb
Th sylems
CSnlaumod
CnsidorL
on doruyatives, - we
system fvo
second onclar dertial e
two wnknswn
h orm
o,) dtv a,( +(4) +
at) +
a t)y =
F
b4)+b5 t)y F£) =
e 2 d 5
dtr+5
dtv
+ 7 + 3+27=
olt
3t+|
3 o
2 +5+2-y-0
System Of ODE
Handwritten Notes
By Sanjibon Hazarika
,D:eretia OpeoTor omod operato athad
malhod
The Gmenal imer syslem
two firu ortdlo DE two
ww known wnetions
+he om
a,(t) + alt) a,(t)x + a,lt)y - F )
b(t) dt
,)+bt)
dt +b,=F
V
2 2 dL3 2x+
= t
d -2 +3+
We shall that soltionn
s O
euot ion OO O orolarad palr
o
mafios gsweh that
of
- 4 (t)y- Simultoma.ous
sst
both e o Hho sytem O o
somo Ral indaLvod a t b
, Tho gemera meas stem
thora t ordloru DE thraa wnknowh
wnctians mc z
or
a,4)ax
+a)a9+a,6)+ ag) *
at) z = F()-
t
b,t)z Ft)
c,e) Cc)+ +e,(0x +)y+|
e
d-2+d
t+
+2-
3-z -t
lt d5 +4y - 5z =
Sint
d 2 + - 3 +2y
-Z =eot
dt
, Asol stemD
rao unefion
orolarad frupa e
(+,3, sueh hat - {lt), Fg
ound z=
ht) Simutamaosly
euaton
tha Syslem
SomO roal intaruva& atb
Th sylems
CSnlaumod
CnsidorL
on doruyatives, - we
system fvo
second onclar dertial e
two wnknswn
h orm
o,) dtv a,( +(4) +
at) +
a t)y =
F
b4)+b5 t)y F£) =
e 2 d 5
dtr+5
dtv
+ 7 + 3+27=
olt
3t+|
3 o
2 +5+2-y-0
