3

I have a partial differential equation:

$$\left(x^2+y^2\right)\frac{{{\partial ^2}u(x,y)}}{{\partial {x^2}}} + x^2\frac{{{\partial ^2}u(x,y)}}{{\partial {y^2}}}=0$$

How to change from Cartesian to Polar coordinates in MMA? Is there such a function in MMA ?

eq=(x^2 + y^2)*D[u[x, y], {x, 2}] + x^2*D[u[x, y], {y, 2}] == 0

there such a thing Laplacian function but in this equation don't helps.

Laplacian[u[r, \[Theta]], {r, \[Theta]}, "Polar"] // Expand

I,m find this in help center:

Manipulate[
With[{vars = 
ToExpression /@ 
 CoordinateChartData[{Coordinates, 2}, 
  "StandardCoordinateNames"]}, 
Simplify@Laplacian[f @@ vars, 
vars, {Coordinates, "Euclidean"}]], {Coordinates, 
First /@ CoordinateChartData[{All, 2}]}, 
FrameLabel -> "Laplacian in Two Dimensions"]

but only works with Laplacian not my equation.

J. M.'s missing motivation
  • 124,525
  • 11
  • 401
  • 574
Mariusz Iwaniuk
  • 13,841
  • 1
  • 25
  • 41

0 Answers0