Question

dy/dx = y/(x+1)(x+2) differential equation

Answer 1

looks seperable to me

Answer 2

1/y dy = 1/(x+1)(x+2)

Answer 3

yep

Answer 4

integrate both sides :)

Answer 5

might want to partial out the right side ... but yes

Answer 6

i dont know how to integrate the right hand side...

Answer 7

erm, my partial fractions is a bit rusty...

Answer 8

left hand side = lny

Answer 9

\[\frac{f(x)}{(x-a)(x-b)}=\frac{A}{(x-a)}+\frac{B}{(x-b)}\]

Answer 10

so A/(x+1) +B(x+2)n is the right hand side

Answer 11

\[\frac{1}{(x+1)(x+2)}=\frac{A}{(x+1)}+\frac{B}{(x+2)}\]
\[1=A(x+2)+B(x+1)\]
solve A and B for x=-1, and x=-2

Answer 12

ahhh ok

Answer 13

1 = A(-1+2) + B(-1+1) ; A = 1

1 = A(-2+2) + B(-2+1) ; B = -1

\[\int\frac{1}{x+1}-\frac{1}{x+2}\]

Answer 14

ohkay i see, so now

Answer 15

ln y = ln(x+1) -ln(x+2)

Answer 16

correct, the base e it all

Answer 17

oh i forgot to mention y=2 when x=1

Answer 18

so i find C first dont i?

Answer 19

ln y = ln(x+1) -ln(x+2) +C

Answer 20

if you have intial conditions, then sure

Answer 21

ln2 = ln2-ln3 +C

Answer 22

C= ln 3

Answer 23

???

Answer 24

ln y = ln(x+1) -ln(x+2) + ln3

Answer 25

y= (x+1) -(x+2) +3

Answer 26

is that the answer?

Answer 27

ps i like your picture :)

Answer 28

\[\Large e^{lna-lnb+c}\]
\[\Large e^{ln(a/b)+c}\]
\[\Large \frac{a}{b}*c_1\]

Answer 29

thnx :)

\[y = \frac{c(x+1)}{c+2}\]
and solve the initial condition

Answer 30

x+2 under there ... that is

Answer 31

so y = { (x+1)/(x+2) } multiplied by 3

Answer 32

that does sound better,

Answer 33

so \[y= 3(x+1)/x+2\]

Answer 34

yaaaaayyyyyyyyyyyy :) thank you. i am a fan

Answer 35

lets step back, and you tell me your initial condition

Answer 36

i got stuck because of the partial fractions bit. my inital conditions are y=2 when x=1

Answer 37

where do i put these conditions in?

Answer 38

\[2 = \frac{c(1+1)}{1+2}\]
\[6 = 2c\]
yep

Answer 39

your way was fine :) i was just making sure

Answer 40

oh so you can also put int the conditions at the end! that's easier i think. because my book is telling me to put in the conditions immediately after integrating. because its a silly book.

Answer 41

good luck :)

Answer 42

thank you very much. do u want a medal?

Answer 43

want? thats not up to me, the thank you is good enough

Answer 44

thanks very much once again :) you're really helpfull. ill probably be back for more later.

Answer 45

see you xxxxxxx

Answer 46

:)