NDSolve[{f[z]gg[r]-8gg[r]-2f[z]gg[r]-Cos[z]gg[r]Sin[z][z]+2r[r]0,f[z]+4-2f[z]-Cos[z]Sin[z][z]-[r]+2gg[r][r]0,f[0]f[2Pi],gg[10]0.0001,gg'[10]-0.0001},{f,gg},{r,0.01,10},{z,0.0,2Pi}(*,MaxStepSize0.01*)]
4
r
2
Cos[z]
2
f[z]
4
r
2
Sin[z]
4
r
′
f
2
f[z]
′
gg
4
r
2
Cos[z]
2
gg[r]
2
f[z]
2
gg[r]
4
r
2
gg[r]
2
Sin[z]
4
r
2
gg[r]
′
f
2
r
2
f[z]
2
′
gg
2
r
2
f[z]
′′
gg
NDSolve::dvlen:The function f[z] does not have the same number of arguments as independent variables (2).
NDSolve[{f[z]gg[r]-8gg[r]-2f[z]gg[r]-Cos[z]gg[r]Sin[z][z]+2r[r]0,f[z]+4-2f[z]-Cos[z]Sin[z][z]-[r]+2gg[r][r]0,f[0]f[2π],gg[10]0.0001,[10]-0.0001},{f,gg},{r,0.01,10},{z,0.,2π}]
4
r
2
Cos[z]
2
f[z]
4
r
2
Sin[z]
4
r
′
f
2
f[z]
′
gg
4
r
2
Cos[z]
2
gg[r]
2
f[z]
2
gg[r]
4
r
2
gg[r]
2
Sin[z]
4
r
2
gg[r]
′
f
2
r
2
f[z]
2
′
gg
2
r
2
f[z]
′′
gg
′
gg