Ordinary or Partial Differential Equation

[Guest]

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

Is this ODE or PDE?

[Guest]

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

[HallsofIvy]

What, exactly is your question and why did you post it? Are you asking whether it is a partial or ordinary differential equation? On the face of it it is a partial differential equation because it has partial derivatives. But both derivatives are with respect to x! It can be treated as an ordinary differential equation with any other variables treated as constants.

But why do you have the same derivative written twice? [tex]\frac{\partial y}{\partial x}+ \frac{\partial y}{\partial x}= 0[/tex] is exactly the same as [tex]2\frac{\partial y}{\partial x}= 0[/tex]. And we can divide by 2 to get [tex]\frac{\partial y}{\partial x}= 0[/tex] which has general solution y= constant or, more generally, y can be a function of other variables but not x.

I wonder if this was not supposed to be something like [tex]\frac{\partial z}{\partial x}+ \frac{\partial Z}{\partial y}= 0[/tex]. That would be a more interesting equation!