Very simple D.E.

[Jameson]

Find a solution to the following D.E.

$$\frac{dy}{dx} + \frac{x}{y}=0$$

$$\frac{dy}{dx}=-\frac{x}{y}$$

Separate variables...

$$ydy = -xdx$$

Integrate both sides...

$$\frac{y^2}{2}=-\frac{x^2}{2}$$

Multiply both sides by 2, and here is where my problem arises...

$$y^2=-x^2$$

Stuck. $x^2$ will always be positive, so after applying the negative, I can't take the squareroot. It has to be a simple mistake. Please give a small bit of help or a small hint.

 

[Dr Avalanchez]

Aaargh... nearly there...

$$y^2=-x^2+C$$

Does this ring a bell?

 

[Integral]

Is there some reason you must restrict yourself to the reals? Even with the constant of integration which you need (as above) there is the possibility of a complex solution. A complete problem statement will include the boundary conditions or initial values. You have not provided a complete problem statement. Without that. your solution is complete with the addion of the constant of integration.