Homework Help: Very simple D.E.

Jameson · Sep 16, 2005

Find a solution to the following D.E.

[tex]\frac{dy}{dx} + \frac{x}{y}=0[/tex]

[tex]\frac{dy}{dx}=-\frac{x}{y}[/tex]

Separate variables...

[tex]ydy = -xdx[/tex]

Integrate both sides...

[tex]\frac{y^2}{2}=-\frac{x^2}{2}[/tex]

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

[tex]y^2=-x^2[/tex]

Stuck. [itex]x^2[/itex] 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 · Sep 16, 2005

Aaargh... nearly there...

[tex]y^2=-x^2+C[/tex]

Does this ring a bell?

Integral · Sep 18, 2005

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.

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Homework Help: Very simple D.E.

Jameson

Dr Avalanchez

Integral