Question

please help me solve the initial value problem y' = x^3(1-y) , y(0) = 3

Answer 1

just separate the variables
\[\Large \frac{dy}{1-y}=x^3dx\]
integrate both sides
can you do this now?

Answer 2

one sec, lemme give it a go

Answer 3

would be fun to use laplaces here :D

Answer 4

nah, have to brush up on my separable equations

Answer 5

it would be great with Laplace:P

Answer 6

@IStutts can you do this or should i guide you ?

Answer 7

it seems it can also be solve by linear DE

Answer 8

yes you can solve this with integrating factor as well.

Answer 9

A little guidance please. should I got Ln|1-y|?

Answer 10

that was soooo close...

Answer 11

yes you should get -ln(1-y) :P

Answer 12

BLAST!

Answer 13

haha

Answer 14

then on the other side i would get x^4/4?

Answer 15

+c

Answer 16

you forgot the constant C

Answer 17

yes !!

Answer 18

haHAAAAA

Answer 19

pellete.... so then i e to both of those equations? e^(-ln|1-y|) = e^(x^4/4)*e^c

Answer 20

which cancels out the ln on the left side?

Answer 21

it will but it will be okay if you write the left side as
ln(1-y)^-1
e^ln(1-y)^-1
1/(1-y) !!

Answer 22

not quite sure why you did that

Answer 23

so in the end, i get y = 2e^(-x^4/4) +1?

Answer 24

sorry i was busy with other question

Answer 25

ok, i am posting a new one that i need assistance through

Answer 26

ok post it.

Answer 27

BOOM!