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WTW256: LU 1.4: SUBSTITUTION METHODS Lecture notes R80,00
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  3. University Of Pretoria (UP)
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  5. WTW 256 - Differential Equations

Class notes

WTW256: LU 1.4: SUBSTITUTION METHODS Lecture notes
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Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover the different substitution methods and how to identify them.

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Document information

  • July 11, 2022
  • 16
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

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1. 4. substitution Method 's
example
How to solve b- f- in
①
4¥
"
:

(2×139) form

=F( 2k13g ) 1) dy =
Flake byte)
DX
① dy = y
-
×


DI Yt "
'




substitution



:÷ ① y=axtby7C
to reduce initial Df
( i. t.ci .




Randy ) to a
F
separable D- f.




ycoj.at#dkdY=FlUIwithy=,,yy
L
'
①
=

( Nyt } )


, }
FI
DX

,2)
% %)
=
f- ( → homogeneous first
,, order D. E.


µ=y to get to seperdble BE
I
solve dy =
Y
To, yix
↳ put in format can
recognise
you
.




①
facto rising mon
'
dy Y -
l
I
=




J,, the fraction .




¥ 1 I
②
Fly ) =
4

441
-1
u= c y=u.x
PRODUCT RULE
③ dy
o-i-tiofe-Y.CI ) .



dy
¥ N -




=
=
U-
tde
, .




Rearrange to get dyyda >

=
( easier)
y me
. . .




¥ ¥ →¢ y
= a




,, ,,
>




?⃝

, ④ ¥ :#
=

"
.




÷ :÷÷
+ . "
a .




¥n
foperab
this side



4)
÷÷÷¥:#
-




uy ,




ul
⑤
)
1 i u
dy
:(
-

u
- -




/ simplify
Toi um


¥ ( -4¥ )
⑥
fY÷z dU://z.dz/seperdte
.




%) # day !
II.
tan
'
(4) =
1h12 It C.
¥1 hwy 4)
-

-



←




d
will always
be
-10
41^(9%111) (1) In 1×17
'
c.
tan
-




¥
=




In
-




implicitsolution .




Too much work to go further .

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