$$(x ^{2}- xy+y ^{2})dx-xydy=0$$ solve de

Question

turingtest · Answer

$$(x ^{2}- xy+y ^{2})dx-xydy=0$$$$(x ^{2}- xy+y ^{2})=xy\frac{dy}{dx}=xyy'$$$$\frac xy+1+\frac yx=y'$$now we sub in $\large v=\frac yx$ from which we get$$y=vx\to y'=v+xv'$$and plug that into the DE

anonymous · Answer

thank you..i ahve a problem the the DE where u cant saparate xy

turingtest · Answer

do you see how I did it above?
do you get it now or do you need more help?

anonymous · Answer

ive solve it

anonymous · Answer

how do i do this $$3x(xy-2)dx+(x ^{3}+2y)dy =0$$

turingtest · Answer

what is the difference?
should be the same procedure

anonymous · Answer

ok. let me try it

turingtest · Answer

Man, sorry, this is an exact differential equation, so that previous method won't work this time I have to go teach a class right now, so here's a link for exact DE's http://tutorial.math.lamar.edu/Classes/DE/Exact.aspx you still need to get dy/dx together first though good luck!