# Differential equation query

1. Jan 24, 2012

### fran1942

Hello, regarding the differential equation: "dy/dx = -x/y"
The general solution is y^2+x^2 = c.

I am wondering why it is expressed this way instead of "y=-x^2+c" ?
I thought you had to seperate the x and y to opposite sides of the equation ?

Thanks for any help.

2. Jan 24, 2012

### tiny-tim

hello fran1942!

(you mean y = √(c - x2) )
no, there's nothing special about y …

the answer is a curve (in this case, a circle), and x2 + y2 = c is a more natural way of describing a curve

3. Jan 25, 2012

### JJacquelin

dy/dx = -x/y
y*dy = -x*dx
y²/2= -x²/2 +C
y² = -x² +c (c=2C)
y²+x² = c

4. Jan 26, 2012

### HallsofIvy

Staff Emeritus
Well, it wouldn't be expressed that way because those are not at all the same!
I presume you meant $y= \sqrt{c- x^2}$. The difficulty with that is that it is only "half" of the solution- the other half would be $y= -\sqrt{c- x^2}$.

No, differential equations often have solutions that are not functions.