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.

Log in or Sign up

Very simple D.E.

Jameson

Dr Avalanchez

Integral

Very very very simple question .for you (Replies: 1)

Very Simple Airplane problem (Replies: 7)

Very simple - mass on a spring (Replies: 5)

Very simple conversion problem (Replies: 9)

Very simple entropy question (Replies: 2)