Solving ODE which is a sum of Biharmonic and laplace DE
I am looking for solution of ODE with variable coefficients. The form of the equation is as follows:
Bi-harmonic-equation+ Constant * Laplace-equation = 0, which is can be written as
D4 w+ C* D2w=0
where D4= D2*D2, where the differential operator D2= d2/dx2 + 1/r d/dx
Since I am new I am not able to type in proper mathematical format for easy understanding.
operator D4 is equation (7) in the following link.
Biharmonic Equation -- from Wolfram MathWorld
and operator D2 is equation (3) in the following link.
Harmonic Function -- from Wolfram MathWorld
Could any one give me inputs for general solution to this differential equation.