Question

please help with integration!! :) see differential equation below

Answer 1

\[\frac{ 21 }{ 95-2v } .\frac{ dv }{ dt } =1\]

Answer 2

are you trying to solve that differential equaiton ?
whats the complete question ?

Answer 3

yep - im trying to solve it.... hang on a sec...

Answer 4

shouldnt a logistics DE be in the form: \[\frac{ dP }{ dt }=kP (\frac{ A-P }{ A })\]

Answer 5

yes, just separate variables

Answer 6

\[\large \frac{ 21 }{ 95-2v } .\frac{ dv }{ dt } =1\]

\[\large \frac{ 21 }{ 95-2v } dv =dt\]

Answer 7

integrate both sides

Answer 8

\[\large \int \frac{ 21 }{ 95-2v } dv =\int dt\]

Answer 9

right side evaluates to \(t+C\)

Answer 10

\[\large 21 \int \frac{ 1}{ 95-2v } dv = t+C\]

Answer 11

you still need to evaluate the left side integral

Answer 12

\[21\ln |95-2v|(\frac{ 1 }{ -2 })\]

Answer 13

Looks good !

Answer 14

ok ill keep going on paper and let you know what i get....

Answer 15

okay, you need to solve \(v\) all by itself

Answer 16

almost there

Answer 17

oooh thats how you do the constant thingo...

Answer 18

so to find c5 I know that (0,0) satisfies

Answer 19

Got it... theres a mistake in your working I think....

Answer 20

for row 3, I but and A infront of the e

Answer 21

yeah does above look good ?

Answer 22

\[\large 21\ln |95-2v|(\frac{ 1 }{ -2 }) = t + C\]

\[\large \ln |95-2v| = \frac{-2}{21}t + C_2\]

\[\large 95-2v = e^{\frac{-2}{21}t + C_2}\]

\[\large -2v = C_3e^{\frac{-2}{21}t }-95\]

\[\large v = -\frac{C_3}{2}e^{\frac{-2}{21}t }+ 47.5\]

Answer 23

yep... now its good

Answer 24

Finally !

Answer 25

\[\frac{ -95(e ^{-2t/21 }-1) }{ 2 }\] is my final equation

Answer 26

haha yea!

Answer 27

matching !! so how do you find the maximum velocity ?

Answer 28

well i think i have to do as t--> infinity then e^-infty aproaches 0 so i'm left with 95/2

Answer 29

what about 171 kph ?

Answer 30

well 95/2 is in m/s so just multiply by 3.6 and voila 171kmphr

Answer 31

haha - I have been answering my own questions.... thanks for taking me through the steps ganshie8!!

Answer 32

I see, you have been answering my questions also lol !

Answer 33

LOL – yeah I'm totally an honorary professor of maths..... thanks as always!! :)

Answer 34

:D