# Very simple D.E.

Gold Member
MHB
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.

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