Write a complex PDE with proper format for NDSolve?

Questions
,
1

Hello, I would like to write the given PDE for NDSolve,

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with the given initial conditions:

psi(r,0)=1
psi(0,phi)=0

psi’(r,0)=0
psi’(0,phi)=0

psi’‘(r,0)=10
psi’'(0,phi)=10

How do I write that in NDSolve form?

I tried the following test:

uval =  NDSolveValue[{i*r^3*D[u[r,y],r,r,r]+r^2*D[Tan[y]*u[r,y],r,r]+r*D[Tan[y],r]*r*i*D[u[r,y],r]+r*i*D[(Tan[y])^2*u[r,y],r]+Tan[y]*r*i*D[u[r,y],r]+Tan[y]*r*i*D[Tan[y]*u[r,y],r]+(Tan[y])^2*r*i*D[u[r,y],r]+(Tan[y])^3*i*u[r,y]==2*u[r,y]*r^2/(Cos[y])^5, u[r, -3] == u[r, 3] == u[-3, y] == u[3, y] == 0}, u, {r, -3, 3}, {y, -3, 3}]

However it says:

“NDSolveValue::femcmsd: The spatial derivative order of the PDE may
not exceed two.”

Thanks!

2

Hi, in order to solve the following

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I used :

uval = NDSolveValue[{ir^3D[u[r,y],r,r,r]+r^2D[Tan[y]u[r,y],r,r]+rD[Tan[y],r]riD[u[r,y],r]+riD[(Tan[y])^2u[r,y],r]+Tan[y]riD[u[r,y],r]+Tan[y]riD[Tan[y]u[r,y],r]+(Tan[y])^2riD[u[r,y],r]+(Tan[y])^3iu[r,y]==2u[r,y]*r^2/(Cos[y])^5, u[r, -3] == u[r, 3] == u[-3, y] == u[3, y] == 0}, u, {r, -3, 3}, {y, -3, 3}]

however I get:

NDSolveValue::femcmsd: The spatial derivative order of the PDE may not exceed two.

Can this be done another way?

Thanks