solve the following DE 4y+yx^2-(2x+xy^2)y' I know this is the ODE where u have to 1st test for exactness and I did that and found that it is not exact, now I am struggling to get the integrating factor that will make it exact.

Question

solve the following DE 4y+yx^2-(2x+xy^2)y'    I know this is the ODE where u have to 1st test for exactness and I did that and found that it is not exact, now I am struggling to get the integrating factor that will make it exact.

anonymous · Answer

@experimentX ..help me please

experimentx · Answer

http://www.sosmath.com/diffeq/first/intfactor/intfactor.html

experimentx · Answer

worst case ... your IF is function of both x and y ...this case don't try!!

anonymous · Answer

What u implying is that I can get the intergrating factor by jst checki, or u mean I don't have to?

experimentx · Answer

if ... it is of neither form, then probably it must of some both function of x and y ... I'm not quite familiar on solving the last case.

anonymous · Answer

how to check for both then?

experimentx · Answer

you have two cases that determine if the integrating factor is only function of x or only function of y ... 

go to the link i posed above.

anonymous · Answer

cool

anonymous · Answer

Ok cool I get what u saying....the 2cases are easy and the third is not...

experimentx · Answer

yep.

anonymous · Answer

why do you say that it is an ODE where you need to check whether it is exact or not ?

You can also try a different approach using y=vx

Say if its not exact then instead of 2 cases you have 4
a) IF (Intergrating Factor) depending on x 
b) IF  depending on y
c) IF depending on xy both
d) IF depending neither on x nor y