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\[\frac{ dy }{ dx }+2xy=x\]

for integrating factor, your equation needs to be in the form of
\[\frac{dy}{dx} + p(x)y =q(x)\]

wait let me recheck that formula

ok it's good

integrating factor seems to be the best choice on here.. your equation looks like it's in that form

dydx+2xy=x for this question how can you can tell which method to use?

i used integrating factor but apparently the solution is by separation of variables. i'm confused.

\[\frac{ dy }{ dx }+2xy=x \] try subtracting 2xy on both sides and factor out an x

you are supposed to get the same solution regardless of what method you are using

really? so that means i'm something wrong in my solution

oh i see, i'll try doing them again. Thanks for clarifying :)

|dw:1435302171281:dw|

You can use this attached file as a reference guide. ODEs is the only magician Math course because no matter what method you choose, you will always get the same result.
If I remembered correctly, each type of equation has certain characteristics and rules, so you may need to memorize what they are so you can be able to figure out which method is best to solve these ODEs.

sorry I spotted an error x( - fixed it