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Can I divide each term by 1/dy to separate?

This is in the form m+ny'=0

see if its exact

Start by isolating y' .. then integrate both sides

if they are equal then it is exact

But to isolate y' I would need to divide each term by y' correct?

wait...is this cal 1 or differential equations and linear algebra

Calc II differential equations

http://1337.is/~gaulzi/tex2png/view.php?png=201103312034348813.png would look like this isolated

Well you can try implicit differentiation.

take the derivative of the first term with respect to x

kristin wouldn't it be -x^2?

sorry yes, thats correct, minor typo :)

Ok no problem. Thanks

I can toss up for you the answer if you want :)

y' is dy/dx correct? If i were to rewrite it

yeah

Ok so if I were to solve y'+y=10 would I just replace y' with dy/dx and then move it all around?

I'm trying to figure out the steps

it can be done by the separable variables method

after some modification you can get
dy=-x^2/(x^3+8) dx
just integrate both sides

I know the answer I'm trying to figure out the steps, could you show me the steps kristin? Plz.

I can show it to you

did you integrate like she said?

I know I need to integrate each piece, I just need to know how to get each piece by itself

do a u substitution

u=x^3+8
du=3xdu

du=3x^2 sorry

you should get: integral( -1/3(1/u) dx

now just substitute for u=x^3+8
\[y=-1/3\ln \left| x^3+8 \right|+c\]

Oh right I got that. Thanks

np