Def Eq Solve: (2xy+x)dx+(x^2+y)dy=0

Question

anonymous · Answer

2xy dx+x^2 dy   + xdx+ydy=0
Observe that dervative of x^2 y=2xydx+x^2dy(The first two terms)
d(x^2 y) + xdx+ydy=0
integrate
x^2y+(x^2+y^2)/2=0

anonymous · Answer

Omg why are you so fast at this xD Im still pretty lost though on this

anonymous · Answer

lol. integral of dx=x so integral of d(x^2 y) is also x^2 y.

anonymous · Answer

well not exactly this problem but other ones where you may not be able to observe that? or will there always be something like that

anonymous · Answer

Well there are some standard stuff like xdy-ydx/x^2=d(x/y) and all.

anonymous · Answer

yea is there another way you could possibly show it assuming I will most likely not see that while I'm doing my test xD

anonymous · Answer

Just learn the standard results for the test its not very hard to identify, all equation are always solvable.

anonymous · Answer

I can do that a lot with calc but for some reason DE is just not sinking in at all... lol