An equation of Exact.

[farm]

Hello every body;

I have trouble with exact differential equation problem I have spent a day to solve it but I could not, well math is not my major but I should understand Differntila Equations as a part of my Graduate Researsh.

Problem Is:

Determine wether the equation in this problem is exact. If it exact, find the solution?

xdx/( x^2+ y^2)^(3/2) + ydy/ ( x^2+ y^2)^(3/2) = 0

well i did like this
for exactness
I multiplied through by ( x^2+ y^2)^(3/2) to rid of it but when I complete the answer the answer I get x^2 + y = c which is wrong answer
(right answer x^2+y^2=c)

can you help me please the due is tommorow

 

[tkhunny]

1) How did you get "y" when the exact same structure in 'x' produced x^2?

2) "Get rid of it"? Is that a mathematical operation? I'm not aware of it.

 

[Deleted member 4993]

Hello every body;

I have trouble with exact differential equation problem I have spent a day to solve it but I could not, well math is not my major but I should understand Differntila Equations as a part of my Graduate Researsh.

Problem Is:

Determine wether the equation in this problem is exact. If it exact, find the solution?

xdx/( x^2+ y^2)^(3/2) + ydy/ ( x^2+ y^2)^(3/2) = 0

well i did like this
for exactness
I multiplied through by ( x^2+ y^2)^(3/2) to rid of it but when I complete the answer the answer I get x^2 + y = c which is wrong answer
(right answer x^2+y^2=c)

can you help me please the due is tommorow

A DE to be exact would be of the form

f(x,y)dx + g(x,y) dy = 0

and

f[sub:2nrjfmi7]y[/sub:2nrjfmi7] = g[sub:2nrjfmi7]x[/sub:2nrjfmi7]

Start from there.

 

[farm]

1) How did you get "y" when the exact same structure in 'x' produced x^2?

2) "Get rid of it"? Is that a mathematical operation? I'm not aware of it.

Well I solve it as My= Ny and I really did well after I handed in my homework. so I have

My = -3/2 ( x^2 + y^2) ^-1/2 and Nx= -3/2 ( x^2 + y^2) ^-1/2 so they are exact but the integration of :

integrate x dx/ (x^2 + y^2)^3/2 is the rest of the solution



Thank you I just get nowww !!!: bad luck (- -)