Question

Determine if following equations is exact. If it is exact, solve it:\[\frac{x\text d x}{(x^2+y^2)^{3/2}}+\frac{y\text d y}{(x^2+y^2)^{3/2}}=0\]

Answer 1

Is the final result equal to x^2 + y^2 =c ??
where c is constant

Answer 2

i am not sure the back of my book dosent have the answer to this problem,
your answer looks nice though, how did you get it

Answer 3

A closer look at your question shows that the equation is nothing more than xdx+ydy=0.......(1)
Now you just need to integrate the above equation (1) on both sides.. you will get the result.. that's all..

Answer 4

\[\frac{x\text d x}{(x^2+y^2)^{3/2}}+\frac{y\text d y}{(x^2+y^2)^{3/2}}=0\]\[x\text d x+y\text d y=0\]\[y\text d y=-x\text d x\]\[\int y\text d y=-\int x\text d x\]\[\frac{y^2}2=-\frac{x^2}{2}+c_1\]\[x^2+{y^2}=c_2\]

Answer 5

yeah, you got it..

Answer 6

hmmm
are you sure this is right

Answer 7

Almost.. What i doubt a bit is that are you allowed to cancel out (x^2 +y^2).. But then you can cancel them out if both x and y are not zero simultaneously.. And both X and Y are never zero in such equations.. That will make it too absurd..
So, i am 99% sure the solution is correct..

Answer 8

Well the solution is correct for all cases where X and Y are not zero simultaneously..

Answer 9

And if they are zero simultaneously, the equation can never be solved..

Answer 10

Am is supposed to play dart?

Answer 11

well the solution was x^2+y^2=c
graphically this corresponds to circles of radius c where i have drawn 4 values of c

Answer 12

yeah. lol..

Answer 13

*r^2

Answer 14

Yeah, that is the solution graphically...