Solving a Partial Differential Equation

[YongL]

A partial differential equation.

 

[Roberto Bramb]

It is the Laplace equation in cylindrical coordinates with symmetry about y-axe.
You can solve it by variable separation, once given the boundary condition:
phi(x,y)=X(x)Y(y)

X''+X'/x+cX=0 (in x, 0-order Bessel equation)
Y''-cY=0 (in y)
c=arbitrary positive/negative real constant

 

[YongL]

Thanks, roberto, i got it