Question

ODE integrating factor question? http://i.imgur.com/kNp3e.jpg

Answer 1

I got the integrating factor be x^3

Answer 2

I did end up finding the solution, I misread the question thinking I needed to find the solution. But I how I do prove I am correct.

Answer 3

I can't exactly say, use Wolfram on my exam haha!

Answer 4

just take the derivative of\[\frac d{dx}(yx^3)\]using the product rule

Answer 5

whaddya get...?

Answer 6

Letting u=y and v=x^3

y*3x^2+x^3dy/dx

Answer 7

now factor out x^3

Answer 8

You mean like x^3(y3x^2+dy/dx)

Answer 9

that is not the right way to factor out x^3 from that expression, watch your algebra

Answer 10

y(3x^2)+x^3(dy/dx)
^^^^
gotta deal with this term too!

Answer 11

Aw crap.

Answer 12

Integrate both terms?

Answer 13

no, I am just telling you to factor x^3 out of y(3x^2)+x^3(dy/dx)

Answer 14

you almost had it above, but you neglected the first term

Answer 15

@TuringTest x^3(3/x) + dy/dx ?

Answer 16

Just coming to terms how poor my basic algebra is...!

Answer 17

almost, but watch your parentheses\[x^3\left(\frac3x+\frac{dy}{dx}\right)\]

Answer 18

oops left out a y\[x^3\left(\frac3xy+\frac{dy}{dx}\right)\]

Answer 19

I really should learn how to use the equation editor, I don't know to do the fraction line.

Answer 20

...and we already know that\[\frac3xy+\frac{dy}{dx}={x^2+1\over x^3}\]from the initial problem, so this tells us that\[\frac d{dx}(x^3y)=x^3\frac{dy}{dx}+3x^2y=x^3\left(\frac{dy}{dx}+\frac3xy\right)=x^3\left({x^2+1\over x^3}\right)\huge\checkmark \]which proves it

Answer 21

if you want to learn to make it look really nice you need to learn the language for math symbols called LaTeX

Answer 22

in that language you can write fractions with either \frac{x}{y} or {x \over y} enclosed on brackets

Answer 23

\[\frac{hey}{dude}\.]
^ take out this point and you get...

Answer 24

\[\frac{hey}{dude}\]

Answer 25

@TuringTest You are my saviour tonight, I can't failed this exam haha. Gonna be a long night!

Answer 26

Gonna try out latex now.

Answer 27

glad I could help
here's a cheat sheet to help you get started using latex
http://omega.albany.edu:8008/Symbols.html
Good luck!

Answer 28

also, if you ever want to know how someone else typed something using LaTeX just hover over the expression
right click -> show math as -> tex commands
that app has been on the fritz lately, so you may need to open it as a separate page to see the coding depending on your browser