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WTW256: LU 1.2: SEPARABLE EQUATIONS R50,00
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  3. University Of Pretoria (UP)
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  5. WTW 256 - Differential Equations

Class notes

WTW256: LU 1.2: SEPARABLE EQUATIONS
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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 separable equations theory.

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Document information

  • July 11, 2022
  • 7
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

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1.2 .
unit Application of
separate DE 's
example -

exponential
growth of population

Newton 's Idw of cooling
- Temp
IT =
Roll -
Tm )
dt time -

Instant ( room
✓ temp .




Diff btw .




rate of →
Directly to → Temp
and room
Change Proportional temp


Torricelli 's law :p raining of a tank .




Achlidh =
-

Asin
Tdt f.
↳
height of
water
Area of
Non-linear b. E.
cross-section
ottdhk .
(square root) -




Most of the time NOT necessary to find explicit
solution

, EXAMPLES
1. Walter ind kettle cools down From C
to
-




too

80
"
in to minutes in a room with temp 251 .




t
1.1 . Find temp of water after 20 mins .




to cool
1- 2 .
How long will it take for water
'
?
'




down to 40
we knew

write mathematical model Newton 's law
=




of
Temp changes cooling
d÷
-




→
with time




÷ KITT Tm )
-


=




' '
KCT - 25 ) I FIFTH
T


initial conditions

) initial
'




C
Tco )=
-


100
'c Value problem
TCI a) =
80

separable Ttp
=
KIT -1514 )
leave constant

£2s ( %)
-

-
he



1h47 -251 )
=
let -1C

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