Transforming a 1st Order PDE into a 2nd Order PDE: A Simple Example

[dvs77]

form the differential equation for the follwing equation
(x^2)/a^2 +(y^2)/b^2+(Z^2)/c^2 =1

 

[Theelectricchild]

Just to keep us busy or what?

Show us your work!

 

[cepheid]

I read that as:

Form the differential equation for the following equation:

\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1

I don't get it...how do you get a PDE out of that?

 

[dextercioby]

No,find the PDE whose solution is the ellipsoid's implicit equation...

Daniel.

 

[cepheid]

I see, ok. That wasn't really clear before.

 

[dvs77]

I mean u get a First order or second order partial differential equation

 

[kleinwolf]

Well for this last question : suppose you have a 1st order PDE, then just derive again and you get a 2nd order one...

The question is a bit ambigous...let's take a simpler exemple, nonparametric :

y(x)=x^2

Then there are an infinity of differential equation having that solution :

y'=2Sqrt(y)

y''=y'/Sqrt(y)

aso...

Moreover I don't know if you want the parametric equation or the explicit version...(ie. x=x(theta,phi) or x=x(y,z)...)

Just plug in this in your equation and differentiate...