1
Title
Class
Mail
1
2
3
4
5
6
7
8
9
10
, Date . . . 1
2 2.
seperable DE 2 .
1 First order linear BE
The sourtion PE
t areFumctionsthat
Vs ) = mls Maass Y 3
2
kg +
PLx了 g <x
3 =
y
2 =
satisfy the DE
solve
x ← :
登
sepercuble
DE of VLX ) if get a
fiy 3 -
s ron lineaz
: ( xct 品 ,
)
+2 y
+
ex ,
“ y (
3y ' = x
g
=
…
≤
won leneaz
2
=
歲 V (x ) =
g V () = 3
Intagrate bsth side Dsolvexy tzxy ' = e
"
=☆+ dprductrulte
C +ε C
3
2
.
[ xcxry ) ex =
Air resistouce constont 3 N .
slm → Fair = 3v 程 4 +c ← implicit
solution
些 xy etC =
4
tC
explicit / general
x
m acceleration =
Ʃ Forces
Y =
瓷 + c ←
Solution
g =
tX gemeralsolution
=
Weight t Fair
=
5
m
收 F3U
u
-
alwaysslow dowy
air
slve eYy = 1 Tey yc )
= 0 ② xe 5"
=
y e
5
xy
'
+
5
e5
xy
=
e
☆
5 cy
' 5y 3
+
the speed ↓
6
=
*
去 1 tey ③ solve
y + 5y = 1 tex
50
↓ x e on poth side
aly
"
) dx
* "y 50
e =
{ te e tex 5y =
e tex
7
gezey dx s
↓
=
= xtc
es
"
y
= te哈 tc
5x
tEY
8
U = { ↓ ÷ e
lu :
eYtdy Y = 5 +
tce -
5x
= luliteY ]
S = lulu )
9
lulltey ) =
xtC
t
implicit sslufion
1 tey extc
=
10
* +c
eY = C - 1
←
) "
λ
e e
=| lm e**
1 C
是 =
-
.
y ( ε
_ ↓
C
y = lu (Ce 1 )
x= 1
Yd 3 = 0
y
= 0
0 =| u ( C .
e -
1 了
= 汁
, Date . . . 1
2 . 3
Given 1
y
'
+
Pcx) y
=
gLx
}
Spcx3 alx
factor
The integrating s
Lx ) =
e
slve tamLx ] sinxcosx
ly
'
=
y
PCx )
↓
ftamcx ) 5∞dx )
2
µcx ) = C
=
e
U = Cosx du :
-iu {x )
efe= eluw
=
µ cx ) = U = cosx
3
d uuultiply by integratins factor
CosLx3
'
-
simlx 3 gunx
y y cos x
-
=
Sx ( cosxy ) wszx ix
4
=
主
csy sx
5
geuercal 崎 twx
C
→ g =
Sp}
umtion
6
7
8
9
10
Title
Class
1
2
3
4
5
6
7
8
9
10
, Date . . . 1
2 2.
seperable DE 2 .
1 First order linear BE
The sourtion PE
t areFumctionsthat
Vs ) = mls Maass Y 3
2
kg +
PLx了 g <x
3 =
y
2 =
satisfy the DE
solve
x ← :
登
sepercuble
DE of VLX ) if get a
fiy 3 -
s ron lineaz
: ( xct 品 ,
)
+2 y
+
ex ,
“ y (
3y ' = x
g
=
…
≤
won leneaz
2
=
歲 V (x ) =
g V () = 3
Intagrate bsth side Dsolvexy tzxy ' = e
"
=☆+ dprductrulte
C +ε C
3
2
.
[ xcxry ) ex =
Air resistouce constont 3 N .
slm → Fair = 3v 程 4 +c ← implicit
solution
些 xy etC =
4
tC
explicit / general
x
m acceleration =
Ʃ Forces
Y =
瓷 + c ←
Solution
g =
tX gemeralsolution
=
Weight t Fair
=
5
m
收 F3U
u
-
alwaysslow dowy
air
slve eYy = 1 Tey yc )
= 0 ② xe 5"
=
y e
5
xy
'
+
5
e5
xy
=
e
☆
5 cy
' 5y 3
+
the speed ↓
6
=
*
去 1 tey ③ solve
y + 5y = 1 tex
50
↓ x e on poth side
aly
"
) dx
* "y 50
e =
{ te e tex 5y =
e tex
7
gezey dx s
↓
=
= xtc
es
"
y
= te哈 tc
5x
tEY
8
U = { ↓ ÷ e
lu :
eYtdy Y = 5 +
tce -
5x
= luliteY ]
S = lulu )
9
lulltey ) =
xtC
t
implicit sslufion
1 tey extc
=
10
* +c
eY = C - 1
←
) "
λ
e e
=| lm e**
1 C
是 =
-
.
y ( ε
_ ↓
C
y = lu (Ce 1 )
x= 1
Yd 3 = 0
y
= 0
0 =| u ( C .
e -
1 了
= 汁
, Date . . . 1
2 . 3
Given 1
y
'
+
Pcx) y
=
gLx
}
Spcx3 alx
factor
The integrating s
Lx ) =
e
slve tamLx ] sinxcosx
ly
'
=
y
PCx )
↓
ftamcx ) 5∞dx )
2
µcx ) = C
=
e
U = Cosx du :
-iu {x )
efe= eluw
=
µ cx ) = U = cosx
3
d uuultiply by integratins factor
CosLx3
'
-
simlx 3 gunx
y y cos x
-
=
Sx ( cosxy ) wszx ix
4
=
主
csy sx
5
geuercal 崎 twx
C
→ g =
Sp}
umtion
6
7
8
9
10
