Question

integrate..

Answer 1

?

Answer 2

\[\int\limits_{}^{}\frac{ dx }{ x+x ^{3} }\]

Answer 3

i think 42

Answer 4

wingspans

Answer 5

get off my question

Answer 6

\[\frac{ 1 }{ x+x ^{3} }\]
\[=\frac 1x\cdot\frac{ 1}{ 1+x ^{2} }\]
now use partial fractions

Answer 7

I factored too. Don't need partial fractions for the test tomorrow so I'm going to move on to another study question. thx

Answer 8

??????????????????????

Answer 9

@cshalvey

Answer 10

1/(x+x^2) = 1/(x*(x+1))

Answer 11

\[\frac 1x\cdot\frac{ 1}{ 1+x ^{2} }=\frac Ax+\frac{ Bx}{ 1+x ^{2} }\]
\[1={ (1+x ^{2}) A+Bx^2}\]
\[1={ A+(A+B)x^2}\]

is x=0

we see 1=A

\[1={ 1+(1+B)x^2}\]
\[0=(1+B)x^2\]
\[B=-1\]

\[\frac 1x\cdot\frac{ 1}{ 1+x ^{2} }=\frac 1x-\frac{ x}{ 1+x ^{2} }\]

Answer 12

is x=0
* 'should be'
when x=0

Answer 13

Thanks for the refresher in partial fractions. I took a year off of school and it has been a year before that since calc 3. My diff eq test tomorrow will not have partial fractions however.

Answer 14

Still nice to see it again for the future

Answer 15

anymore DE questions?

Answer 16

Can you explain in laymens terms how to determine a linear equation. I've read the def'n and I think i kinda get it. but its still iffy

Answer 17

do you mean how to determine if a system is linear?

Answer 18

yes

Answer 19

A differential equation is linear if it can be written in the form \[y'+p(x)y=q(x)\]

Answer 20

ok I just have to learn to recognize that form or manipulate to get that form if possible.

Answer 21

when you look at the DE first check if it is;
separable ,
if not check if it is
linear ,
if not check if it is
homogenous,
....,
...,

Answer 22

this was a trick question\[\frac{ dx }{ dt }+xt=e ^{x}\]I originally thought linear but e^x is not a function of x, correct? That is why it is not linear

Answer 23

Thx for the tips

Answer 24

e^x is a function of x

Answer 25

hmm, The book says this isn't linear can you help explain why not

Answer 26

\[\frac{ dx }{ dt }+xt=e ^{x}\]
changing x into y
and t into x

\[\frac{ dy }{ dx }+yx=e ^{y}\]

to be linear it would have to be e^t

Answer 27

make sense?

Answer 28

oh, good catch.

Answer 29

I wasn't paying close enough attention to what the independent variable was

Answer 30

it can be confusing when they swap the lettes around

Answer 31

I really appreciate the help. I'm going to work through some undetermined coefficient problems. I might post another question if I get stuck

Answer 32

link me in when you do.

Answer 33

will do