Solve the partial differential equation p cos(x+y) + q sin( x+y)=z, where the partial derivatives of z with respect to x,y are denoted by p and q respectively.
Reduce the following PDE to a set of three ODEs by the method of separation of
variables.
∂ ²u/∂ r² + (2/r) ∂u/∂ r + (1/r²) ∂ ²u/∂θ ² + (cosθ /r²) ∂u/∂θ + (1/r² + sin²θ ) ∂²u/∂φ ² = 0